Class 9th Mathematics AP Board Solution
Exercise 8.1- State whether the statements are True or False.(i) Every parallelogram is a…
- Complete the following table by writing (YES) if the property holds for the…
- ABCD is trapezium in which AB || CD. If AD = BC, show that ∠A = ∠B and ∠C = ∠D.…
- The four angles of a quadrilateral are in the ratio 1: 2:3:4. Find the measure…
- ABCD is a rectangle AC is diagonal. Find the angles of ∆ACD. Give reasons.…
Exercise 8.2- In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that…
- Show that the diagonals of a rhombus divide it into four congruent triangles.…
- In a quadrilateral ABCD, the bisector of ∠C and ∠D intersect at O.Prove that…
Exercise 8.3- The opposite angles of a parallelogram are (3x-2)^{0} and (x+48)^{0}…
- Find the measure of all the angles of a parallelogram, if one angle is 24° less…
- In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side…
- In the adjacent figure ABCD is a parallelogram P, Q are the midpoints of sides…
- ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and…
- ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C…
- In delta^{3}abc and DEF, AB || DE, AB=DE; BC = EF and BC || EF. Vertices A, B…
- ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are…
- ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA…
Exercise 8.4- ABC is a triangle. D is a point on AB such that ad = {1}/{4} ab and E is a…
- ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA…
- Show that the figure formed by joining the midpoints of sides of a rhombus…
- In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC…
- Show that the line segments joining the midpoints of the opposite sides of a…
- ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse…
- State whether the statements are True or False.(i) Every parallelogram is a…
- Complete the following table by writing (YES) if the property holds for the…
- ABCD is trapezium in which AB || CD. If AD = BC, show that ∠A = ∠B and ∠C = ∠D.…
- The four angles of a quadrilateral are in the ratio 1: 2:3:4. Find the measure…
- ABCD is a rectangle AC is diagonal. Find the angles of ∆ACD. Give reasons.…
- In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that…
- Show that the diagonals of a rhombus divide it into four congruent triangles.…
- In a quadrilateral ABCD, the bisector of ∠C and ∠D intersect at O.Prove that…
- The opposite angles of a parallelogram are (3x-2)^{0} and (x+48)^{0}…
- Find the measure of all the angles of a parallelogram, if one angle is 24° less…
- In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side…
- In the adjacent figure ABCD is a parallelogram P, Q are the midpoints of sides…
- ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and…
- ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C…
- In delta^{3}abc and DEF, AB || DE, AB=DE; BC = EF and BC || EF. Vertices A, B…
- ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are…
- ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA…
- ABC is a triangle. D is a point on AB such that ad = {1}/{4} ab and E is a…
- ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA…
- Show that the figure formed by joining the midpoints of sides of a rhombus…
- In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC…
- Show that the line segments joining the midpoints of the opposite sides of a…
- ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse…
Exercise 8.1
Question 1.State whether the statements are True or False.
(i) Every parallelogram is a trapezium ( )
(ii) All parallelograms are quadrilaterals ( )
(iii) All trapeziums are parallelograms ( )
(iv) A square is a rhombus ( )
(v) Every rhombus is a square ( )
(vi) All parallelograms are rectangles ( )
Answer:(i) [True]
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⇒ The trapezium has a property
One pair of opposite sides are parallel
This is conveyed by parallelogram
as they have 2 pair of parallel sides
∴ Every parallelogram is a trapezium
(ii) [True]
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACbAbUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiqupEjS7sgkEQPgjt8pppXdhN2RaorztYbiLwhbX8dhNbSLBHI+ordlmQcFn2Z+bjPFegxOskSSK29WUEN6j1rSpT5OpEKnN0H0UUVkaBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRWJ4su7i00dTbzNAZriKF5l4MaMwBIPY47+9NutD06xjjuILp9OkjkX/SDMTv5+6244bPTmtFBWTb3M3N3skbtFFFZmgUUUUAFFFFABWBrmr3FlrNjZJeW1nDcRSO806bgCuMDqPWt+s260k3OvWWpGRdltFJGYyud27HOfbFaU3FS97zImm1oO0meS4SSQ6pbX6AgAwRhQp75wx9q0KaqqowqgD2FOqG7spKyCiiikMKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooApalrOmaNEJdSv7e0RuFM0gXd9B3qCw1zRPEEcsNhqNteAqRJHHICwB45HUV494tS8h8a6k2q7hPJKTatJ0Nv/AABD0wO4HfOazbZbyfVrSPRiW1cSqbYx/eQ55LeiYznPGK744ROj7XmOR4m1X2fKe4J4X0lYUgMMrwIAFhkuJGjAHQbS2K1gABgDAFc95XjD/n507/vlv8KPK8Yf8/Onf98t/hXE5SluzpUUtkdFRXO+V4w/5+dO/wC+W/wo8rxh/wA/Onf98t/hUlHRUVzvleMP+fnTv++W/wAKPK8Yf8/Onf8AfLf4UAdFRXO+V4w/5+dO/wC+W/wo8rxh/wA/Onf98t/hQB0VFc75XjD/AJ+dO/75b/CjyvGH/Pzp3/fLf4UAdFRXO+V4w/5+dO/75b/CjyvGH/Pzp3/fLf4UAdFRXO+V4w/5+dO/75b/AAo8rxh/z86d/wB8t/hQB0VZuqeItG0Uqup6nbWrsMqkkgDEeoHWs/yvGH/Pzp3/AHy3+FeMzJeQaldR6vuXVvNY3Rl+8xzwR6rjGMcYrow9D20+W9jGvV9lHmtc92tNR0bxHZypa3VrqFuw2yojhxz2I7fjSReHtNjkicxyy+Sd0SzTvIsZHQhWJANePeEFupvG+mNpeTNHLm6aPosGDuDn0PGAe+MV7pRWg6M3BSFSkqsVJoKKKK5zcKKKKACuc8d67d+HfC019Yqv2hpEhSR1ysW9gN5HfGfzxXR1DdWlvfWstrdwpPBMpWSNxlWB7EU1uDPA5bu/nnM9xqd/LPn/AFrXThs+2CAPwFd78PPGc1y95pOtX6yNahGguJmAZg2flY9CRjr1INUfFngDTdHihubC5vooHk2vF5oYKMZAUkEjoe9dtp3hPw9a6XHbW2mw+Sw37myzuT3LHkn8a7cRXo1IJQhZnJRpVYSbnK6NuORJVDxurqehU5FOrnX8G2cbeZp95dWL9vLkJH5f/Xpv2TxXYf6i+ttQQdFmXax/H/69cJ1nSUVzf/CT31nxqmh3MQHWSH51/wA/jVy08VaLeYC3qRsf4ZRsP68UAbFFNSRJVDRurqehU5FOoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiis/W9SXSdKmujjeBtjB7selAHNazBD4r8Vw6XLEk9nZfNKHUMM/xf0X866mw0nTdLVl0+wtrQN97yIlTP1wOayPBmmta6Y17MCZ7w7yT129vz5P410dABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAlcPFY2njHxZNc3lrDc2NkNsYlQMD1x19Tk/lW74t1T+zdFdUbE1x+7THUZ6n8v5ipfDOl/wBlaNFEy4mk/eS/U9vwGBQBestPstOi8mxs4LWPOSkMYQH8BVmiigAooooAKKKKACiiigDD8YW32jw3cHGTEVkH4Hn9M1P4auftXh6zkJyyx7D/AMB4/pV69gF1ZT25GRLGy/mK53wFOW0u4tW+9BN/Mf4g0AdTRRRQAVSu9H02+z9psoZCf4imD+Y5q7RQBzr+DbSNvM068urF+3lyEj8v/r037L4rsP8AUXttqCD+GZdrH8f/AK9dJRQBzf8Awk99Z8apodzCB1kh+df8/jV208VaLeYCXqRsf4ZfkP68Vr1Su9H02+z9psoZCf4imD+Y5oAtpIkiho3V1PQqcinVzr+DbWJvM068u7F+3lyEj8v/AK9N+y+LLD/U3ltqCD+GZdrH8f8A69AHSUVzf/CUXtnxquh3MIHWSH51/wA/jV208U6LeYCXqRsf4ZfkP68UAa9FNR0kUNGyup6FTkU6gAooooAKKKKACisDU3lvfFFnpD3EkNqbZ7h1ico0rBgAu4c4Gc4FMsZLa08QpaQTahAJo3AtrhWaNyuMurMSR/I5rX2el/mZ+01OiooorI0CiiigAooooAK47XmbXvE1tosRJggO+cj9f04+prpdVv00zTZ7x+fLX5R/ebsPzrE8F2DraTarcfNPeMSGP93P9Tz+VAHTKqooVQAqjAA7CloooAKKKKACiiigAooooAKKKKACiiigAooooAKKKyfEuqf2Vo0sytiV/wB3F/vHv+AyaAMM/wDFSeM8fes9P/IkH+rfoK7KsLwjpf8AZ2jI8i4muf3j56gdh+X8zW7QAUUUUAFFFFABRRRQAUUUUAFcf4e/0Dxjqlj0WTLKPxyP0auwrj9U/wBA8f2Nz0W5UKfxyv8AhQB2FFFFABRRRQAUUUUAFFFFABRRRQAVSu9G02+z9psYZCf4tuD+Y5q7RQBzj+DbWJt+nXt3Yv8A9M5CR+X/ANek+zeLLD/U3ltqCD+GVdrfn/8AXrpKKAOb/wCEovLPjVdEuYQOskXzr/n8au2ninRbzAS+SNj/AAy/If1rXqjd6Npt9n7TYwyE/wAW3B/Mc0AXEdJFDIwZT0KnIrHn8ZeGba5NtNrtgkoOCpnXg+hPQVy/jnwo9j4auLjQmvFIdftEMMhO6HPz4A5PH6ZrzaJ7fyAYWjEIHG0gKBXZhsL7e/vWscuIxHsbaXPfbqwsdYigmY79nzwXEMhDLnurKe/5GmWuiWtteLeM89xcIpVJJ5S5QHqB2Ga4n4Qpei11NwHGktIn2UH7pfB8wp/s/d6cZzjvXo9YT5oNwvsbRSklKwUUUVkaBRRRQAUUVXv7yPT7Ga7l+5EhY+/oKAOY8TyvrGt2mg27HaGDzEdv/wBQyfxFdZFEkESRRqFRFCqB2ArmPBlnJN9p1u6GZrpyEJ9M8n8+PwrqqACiiigAooooAKKKKACiiigAooooAKKKKACiiigArjdR/wCKj8XxaevzWljzL6E9/wBcD866LXNSXStJmuuN4G2MHux6f59qzfBmmta6WbyYEz3h3knrt7fnyfxoA6HpS0UUAFFFFABRRRQAUUUUAFFFFABXJePIjHDY3yD5oZsZ+vI/9BrraxfF1t9p8OXPGTEBIPwPP6ZoA14ZVmhjlX7rqGH4in1k+F7n7T4ds2JyyJ5Z/wCAnH9K1qACiiigAooooAKKKKACiiigAooooAKKKKACiiigArg5tF0m9+JTCXTLSQIm5t0KkE7M5PHJya7yuP0b9/4+1OXr5asP1Uf0oA69VVFCooVVGAAMACloooAKKKKACiiigArkvF1xJqF/Z6BbN80rh5SO3pn6DJ/KunurmOztZbmY4jiUsx9hXMeELaS/vbvXrpfnmcrFnsO+P0H4GgDqLa3jtLaK3hXbHEoVR7CpaKKACiiigAooooAKKKKACiiigAooooAKKKKACiiqmqX6aZps95JyI1yB/ePYfnQBzOvMde8TW2ixnMEB3zkevU/px9TXYKqooVQAqjAA7CuZ8FWDrazarcfNPeMSCf7uev4n+ldPQAUUUUAFFFFABRRRQAUUUUAFFFFABUN1ALm0mgPSWNk/MYqaigDlfAU5/s66tG+9BNnH1H+INdVXH6D/AKB421Oy6LMCyj8Qw/RjXYUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXH+EP32vaxc9cuRn6sf8K6522Rsx6KCa5PwAu62v5j/HMP5Z/rQB11FFFABRRRQAUUU1mCKWPQCgDm/FzXl6kOk2EMkjSsGmZVJCLnjJ7c8/hW9Y2kdhYw2kQ+SJAo9/euT1u8S51JtM/tM2JgQ3E0ysRmcj92nHZRgkemK6LQNWXWtIhvAAsh+SZB/A44Yf57EVrKlKMVIzjUTk4mlRRRWRoFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFcv4pt77Vr6z0uCCYW24PNMFO0fj7DP5iulkkSJN8jBVyBk+pOB+tczpWnwanquuNdNO7RXuyMrO67BsU4GCMcmrjFNNvoRKTTSXU6aGJIIUhjXakahVA7AU+sTwzd3E8V/bzzNcLZ3jwRTucs6jB5PcjOM+1bdKUeV2HGXMrhRRRUlBRRRQAUUUUAFFFFABRRRQAUUUUAcfrH+geO9Pu+izgKx/NT/MV2Fcn49iZbSzvU+9BNjP1GR+q100cwnslmXpJGGH4jNAE1FcP4ctDeaJZyzaRdXTSA7rj7djd8x5xvz+lduqhVCjoBgVpUgoO1zOE3NXsLRRRWZoFFFFABRRRQAUUUUAFFFFABRRRQBV1OTytKu5Om2Fz+hrD8Bx7dAZu7zt+gA/pWl4lk8vw5fN/0yI/Pj+tV/B0fl+GrY/3yzf+PGgDcooooAKKKKAIbu8trC2kury4jt4Ixl5JWCqo9ya43VvibokbW8emXsVwzSgO0iOkeP8AeIx1xz7VS+LdnfTQaZdpHJLp1s8huVQFgjkDY7Adh8wz2zXm5vLUrzcRMD2Dhs+2O9d2Gwsa0HJysclfESpySUbn0Fp1la2cLtaqALhzNIwcvvZupyev+FOt9PtrW6ubmGPZJdMGlwxwzAYzjoDj864bwRo/iy28L26C+WyiLu0FtPFl4oy2VByOPXHbOK6D+z/Ff/Qbtv8AvwP8K423d6nSkrLQ6Kiud/s/xX/0G7b/AL8D/Cj+z/Ff/Qbtv+/A/wAKko6Kiud/s/xX/wBBu2/78D/Cj+z/ABX/ANBu2/78D/CgDoqK53+z/Ff/AEG7b/vwP8KP7P8AFf8A0G7b/vwP8KAOiornf7P8V/8AQbtv+/A/wo/s/wAV/wDQbtv+/A/woA6Kiud/s/xX/wBBu2/78D/Cj+z/ABX/ANBu2/78D/CgDoqK53+z/Ff/AEG7b/vwP8KP7P8AFf8A0G7b/vwP8KAOiqtf6jZaXaNd391FawJ1klcKPp9axv7P8V/9Bu2/78D/AArg/iJp2vwXtjfatcfbLCKNlWSOPCW8hI5YAcZHAbtj3rSnBTmot2uROTjFySub2tePNI1O90+x0vUIzuuEdpJUeNCQRtGWAHXn8K6xvDuntPPN/pCNcvvmWO5kRXOMZIB9BXgzXFtKPK3pP5nyiJPnaTPYKOTXt/gi01Gx8Habbaru+1xxYZXOWQZO1SfULgfhXTiKP1drlle5hRq+2T5o7Gxa2lvZW6W9rCkMKDCogwBU1FFcTdzq2CiiigAooooAKKKKACiiigAooooAKKKKAOc8dXlha+G5vt11FAWIMIduXYEHCjqTj0qn4R8Y6Hf6dZ6YdRRb3Z5YhlDRs+OBjcBnjHSuK+JFteWvjKW/vg32OaGNLOdv9XGAPnTPRSW598+1crLi/U2dqDdXM3EMMJ3uW7EY6YPOe1d9LCRnS9o52OOpiJRqcnKe7weGrG2hWG3lvYYl+6iXkoC/Qbq1lXaoUEkAY5OTXLWOt69p1hbw6roc80scSrLNC+/cwAyfzq1F400lm23BntW7iaIjH5ZricpS3Z1KKjsdBRVG31nTLvHkX8Dk9t4B/I1dBBGQcipKFooooAKKKKACiiigAooooAKKKKAMHxnJ5fhucf33Rf8Ax4f4Vc8Ox+V4esV6fuVP58/1rJ8fSbdEij7vOP0BresdkNla25dQ4hXC55OAM8UAWqKa0iK6ozqGf7qk8n6U6gAooooAKrR6bYRT+fHZW6S/89FiUN+eKs0UAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABSEAggjIPUGlooArQafY20plt7O3hkPVo4lUn8QKs0UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFADZI0lQxyIrowwVYZBqG2sbOzJNrawwFuvlRhc/lViigAqOWCGdds0SSD0dQakooAybjwvot1kvp8Sk948p/KqR8HQwndYalfWh7BZMj8q6OigDnP7N8UWn/HvrEN0o6LcR4J/Gj+1fE1p/x9aJHcL/et5Ofy5ro6KAOcXxnaxHbfWN7Zt33xZFX7bxLo11gR6hCCeznZ/OtMqGGGAIPY1RudC0q7/wBdp8DH1CAH8xQBcjljlXdHIrr6qcin1z0ngvS9xa1e5tG7GKU8fnTf7C121/48vEDuB0W4Td+vNAHR0Vzn2nxdaf6yys71R3jfaT+f+FH/AAlk1v8A8hDRL23HdlXeP6UAdHRWJb+L9DuOPtgib0lUr/8AWrQbVdOW1kumvrcQRKXeTzRtUDuT2oA5vx6d406AdXlPH5D+tWNWFyvjTSxZCEyiymA84nbjK+lcp4i8c6PqWtafLbLeTWls+XmW3OCNwOQDgngelehaZf6VrsEWq6fJDdKAUWZV+ZPVTnlT0yDWseam7yW5nK01ZMxbv+0D4u0H7etqObjZ5BY/wc5zXVVG8EMksczxI0kWfLcqCUz1we1SUpz5kvL/ADHGPK35hRRRWZYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBWuNOsboH7RaQy57vGCa5Dxt4Dg1DQX/sWzRbyKVJREHIWYKclOTjnt7gV3FFNOzuJq6sfPEglhmMM9rdRTg4MUlu4fPpjHP4V6X8MNB1LS4tR1C/he1S/aPyraQYcBQQXYdicjjrgc13lFddfGTrRUZI56OGhSlzIKKKK4zpCiiigD//Z)
⇒ The quadrilateral is known as
Polygon having four sides
This is conveyed by parallelogram
as they are also four sided polygon.
∴ Every parallelogram is a Quadrilateral
(iii) [False]
![](data:image/jpeg;base64,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)
⇒ The parallelogram has a property
Both pair of opposite sides are parallel and equal
Which is not conveyed by trapezium
as they have only 1 pair of parallel sides
∴ Every trapezium is not parallelogram
(iv) [True]
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACdAWMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2amu6RozyMFVRksxwAKdWb4iUt4d1FVUsTbSYAGc/KaaV3YTdlctwXtrdEi3uYpivXy3DY/Kp65PSWEuvWckc0d2FtXRngg8oQ/d+8f4s4wB2rq6qceV2JhLmQtFFFQWFFFFABRRRQAUUUUAFFFFABUU91b2qB7ieOFScAyOFB/Opawb54LXxKl1qAAtja7IZHXKI+7LD2JGPriqirsmTsjcjkSVA8bK6MMhlOQadWfo32U2bNZ28kEDyuyq4I3ZPLAHoD1HStCk1ZjTugooopDCiiigAooooAKKKKACiiigAooooAKKKKACoJ760tWC3F1DCzDIEkgUkfjU9c9fW1zP4sQ25hTFgctNCZF/1nQcjmqik3qTJtLQ3o5Y5o1kidXRhlWU5B/Gn1HChSJFbbkAA7RgZ9h2qSpKCiiigAooooAKKKKACiiigAooooAx/E3iO28M6WLy4jeZ3cRwwoQDI55xk9BgEk+1clpfxU8y/jh1bTo7W3lcIJ4pi4iJOBuBA4zjkdK6nxZ4Zj8UaUtqZjbzwyCWCbbuCtgjkdwQSDXn/AIb8AT6rqUy6pcQC0sp9ssUO4mcg5xk4wvHPeumkqHs5c/xdDCp7XnXLt1PUf7V07/n/ALb/AL/L/jR/aunf8/8Abf8Af5f8ar/8I3ov/QNt/wDvij/hG9F/6Blv/wB8VzG5Y/tXTv8An/tv+/y/40f2rp3/AD/23/f5f8ar/wDCN6L/ANAy3/74o/4RvRf+gZb/APfFAFj+1dO/5/7b/v8AL/jR/aunf8/9t/3+X/Gq/wDwjei/9Ay3/wC+KP8AhG9F/wCgZb/98UAWP7V07/n/ALb/AL/L/jR/aunf8/8Abf8Af5f8ar/8I3ov/QMt/wDvij/hG9F/6Blv/wB8UAWP7V07/n/tv+/y/wCNH9q6d/z/ANt/3+X/ABqv/wAI3ov/AEDLf/vij/hG9F/6Blv/AN8UAWP7V07/AJ/7b/v8v+NH9q6d/wA/9t/3+X/Gq/8Awjei/wDQMt/++KP+Eb0X/oGW/wD3xQByWufE9bTUZbTSLGO8SB9klxJMVRmHULgHOOma6Pwr4ptvFFjJLHC1vcW7hJ4GO7aSMgg9wR0NcL4v8Bvpd0b3SZoVtbucD7NLkeU7ddpGcrnnHbNdr4O8KL4Xsple4+0Xd0weeQLtXgYCqPQc/XNdM1Q9kuX4uphD2vtHzfCdDS0UVzG4UUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUVQ1bWLXSLfzJ2LO3EcS8s59AKAOP174mmx1Sex0vT0uRbOY5ZppSilh1CgAk4PGfWuh8KeKbfxRYyzJA1vPbvsnhY7tpIyCD3BFed694P1WF21cfZ4V1C6LfZZCwaFn56jPGcnHbNdL4asZfAU00Oq7ZY751Y3sSkIpAwFI7Ac8+9dM1Q9kuX4uphD2vtHzfCd7RTUdXQOjBlYZBByCKdXMbhRRRQAUUUUAFFFFABRRRQAUUUUAFc34T/4+tZ/6/GrpK5vwn/x9az/ANfjUAdJRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHOeNP+Qbaf9fkf9a6Ouc8af8AIOtP+vyP+tdHQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUVg6nrk0l0dL0VRPeH78n8EA9SfWgCfWddTTmW1t4zdX8v+rgX+begqLSdCkjuf7S1WQXOoP0P8MXso/rVjR9Dh0tWlZjcXkvMtw/LMfb0FalAHN+Nf8AkH2f/X4n9a37i3huoHgnjWSNxhlYZBrA8bf8g+z/AOvxP610lAHLFLzwk5eMSXekE/MnV7f3HqK6O1uoL23S4tpFkicZDLUpAYEEAg8EHvXN3Wl3eg3D6hoqmSBjmey7H3X0NAHS0VS0vVrXV7UT2z5xw6HhkPoRV2gAooooAKKKKACiiigAooooAK5vwn/x9az/ANfjV0lc34T/AOPrWf8Ar8agDpKKKKACiiigAooooAKKKKACiiigAooooA5zxp/yDrT/AK/I/wCtdHXOeNP+Qdaf9fkf9a6OgAooooAKKKKACiiigAooooAKKKKACkJCgsSAAMkntTJ7iG1geeeRY40GWZjgCuaL3ni2QrH5lpo4PLdHuPp6CgCS61O71+4fT9FYx26nE972Hsnqa2NL0q10m1FvapgdXc/ec+pNT2trBZW6W9tEscSDAVRU1ABRRRQBzfjb/kH2f/X4n9a6Sub8bf8AIPs/+vxP610lABRRRQBg6poUqXR1TRnFvfD76fwTD0I9as6PrsWqBoZENvexcS278EH1HqK1aydY0KPUitzBIba+i5iuE6/Q+ooA1qKwtK16Rrr+zNXjFtfr90/wTe6n+lbtABRRRQAUUUUAFFFFABXN+E/+PrWf+vxq6Sub8J/8fWs/9fjUAdJRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHOeNP+Qdaf9fkf9a6Ouc8af8g60/6/I/610dABRRRQAUUUUAFFFFABRRSUAZl7q0tvqa2EFqsrmDzizzBABuxjoalutVh0/Thd35WHj7ituJPoPWsjX4oE1y3uZvsEpeDyUgugxJO7OQAp+lX49BgmvIL68RTLDGFSBTmKMjuoIFXLlsrERvd3M+DT7zxJOl7qyNBYqd0Fnn73oz10qoqKFRQqqMAAYAFOoqCwooooAKKKKAOb8bf8g+z/AOvxP610lc342/5B9n/1+J/WukoAKKKKACiiigCjqukWur23k3CfMOUkXhkPqDWTZ6td6Lcpp2uNujY4gvf4X9m9D/n3rpKgvLO3v7Z7a5iWSJxypoAmBBGRyDS1yyzXvhORYrgvd6QxwkvV4PY+o/z7V0sM8VzCs0LrJG4yrKcgigCnd6nJFfpYWtqbi4MfmsC4RUXOASeeSe2O1WLK5kurfzJbaS2kDFWjk6gg9j3Hoao3+m3D6h9ttDC5kg+zzQzEqrrnIII5BGT+dS6Jp0mmWbxSurM8rSbUJKoD0UE84FW+Xl0ITlzGjRRRUFhXN+E/+PrWf+vxq6Sub8J/8fWs/wDX41AHSUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBznjT/kHWn/X5H/WujrnPGn/ACDrT/r8j/rXR0AFFFFABRRRQAUUUUAJXifibX9X1HxBfxz3lzbx2ty8MVvDK0YjCnAJwRkkc5PrxXttYureEdB1y5FzqGnpJOBt81WZGYehKkZ/Gt6FSFOfNJXRlWhKcbRdjhvAWqag8l9cS6bc6xNFIqJePLllBXJTJ7j19CK7T+3tW/6Fu5/7+r/hVaTw9J4fYXfhqJYo1H72xH3JB6j3rY0nWbXV7cyQkrInEkTcNGfQis5yUpNpWLimopNlD+3tW/6Fu5/7+r/hR/b2rf8AQt3P/f1f8K36KgowP7e1b/oW7n/v6v8AhR/b2rf9C3c/9/V/wrfooAwP7e1b/oW7n/v6v+FH9vat/wBC3c/9/V/wrfooA4XxTquoXNnbLNok9uFuVYM0gO488Vt/29q3/Qt3P/f1f8Ki8bf8g+z/AOvxP610lAGB/b2rf9C3c/8Af1f8KP7e1b/oW7n/AL+r/hW/RQBgf29q3/Qt3P8A39X/AAo/t7Vv+hbuf+/q/wCFb9FAGB/b2rf9C3c/9/V/wo/t7Vv+hbuf+/q/4Vv0UAc++t6nKjJJ4YuGRhgqZVII/KvJ9Uv7/wDta/tllu9PghuCEsUnZRFwOTgjJPX8a9Y1HW7i7um0vQ1Etz0luP4IR9fWoP8AhX+g3EYbUbY3d2eZLlpGV3PuVI4rehUjTnzSV0ZVYSnG0XYy/hjrWpalb6hZ3073UdmyCKeQ5YbgSUJ74wD6/NXd1V07TLLSLNbPT7aO2gTkJGMDPcn1PuatVnOSlJtKyLgmopN3CiiioKCub8KkC51ok4AvGyfzroyQASTgCuP8PrDqia/ZwXyKZbpgzxMGIU9e/ccZpoT2NnR9ak1K5mjlhESsPNtTk/vYckBj75H5EVsVkp4esra7tbmyU2z25IwpJDoRgqcnp0P4Vq1U+W/uijzW94WiiioKCiiigAooooAKKKKACiiigDnPGn/INtP+vyP+tXru9v8A+2V0+zFuB9mMxaYMc/NjHBrN8c3EEOnWYlmjjJu0I3uFz19a07rTprjUU1GzvxA3keV/qhIGUndkc1UbX1Jle2hPpWoHUbVpHj8qWKRoZUByFdTg4PcVdqrp9hHp1r5EbM5LM7u5yzsTkk/jVqlK19Bq9tQooopDCiiigAooooAKxNW0J5bgalpcgttQT+Ifdl9mH9a26KAMjR9dTUGa0uoza38X+sgbv7r6itesvWNDh1VFkDGC7i5huE4ZT/UVU0zXJoboaXrSiG8/5Zy/wTj1B9aAN+iiigAooooA5vxt/wAg+z/6/E/rXSVzfjb/AJB9n/1+J/WukoAKKKKACiiobq7gsrZ7i5lWOJBks1AEjMqKWZgqgZJJwAK5u41C88STvZaS7QWKnbPeY+96qlMCXvi2QNIJLTRweE6PcfX0FdLBbw2sKQwRrHGgwqqMAUAQadptrpVqtvaxhEHU92PqT3NW6KKACiiigAooooA4v4pC+PhiP7N5n2Xzx9t8vOfLweuP4d23P+FeX6T9pbWLL+wdp1ESr5Pk9hnndj+DGc54xX0GRkc1Db2NpaMzW1rDCz/eMcYUt9cV1UsR7Om4ct7mE6PPNSvsZGPFnY6Z/wCP0Y8Weumf+P1vUVym5g48Weumf+P0Y8Weumf+P1vUUAYOPFnrpn/j9GPFnrpn/j9b1FAGDjxZ66Z/4/RjxZ66Z/4/W9RQBg48Weumf+P0Y8Weumf+P1vUUAYOPFnrpn/j9GPFnrpn/j9b1FAHgfiP7aviS+/t/b9u8w4L/c8v+DZn+HHp3znmu++EwvRpF75m/wDs8zD7Hu6dPn2/7Oce2c4rt7iytbwKLq2hnCnKiWMNj6ZqZVCgKoAAGAAOldM8Rz0lT5djCFHlqOd9xaKKK5jcKKKKACiiigAooooAKKKKACqep6Xa6tam3uo9w6qw4ZD6g1cooA5q21O88P3CWGssZbZjtgvccfR66RWDAMpBBGQR3qK5tYby3eC4jWSJxhlYda5zN54Skw3mXejk8Hq9v/iKAOpoqK3uIbuBJ7eRZI3GVZTwaloA5vxt/wAg+z/6/E/rXSVzfjb/AJB9n/1+J/WujoAWikrL1jXYtM2wRobi9l4it05JPqfQUAWNU1W10i1M9y+M8Ig+859AKx7XS7vXrhNQ1tdkCnMFl2Hu3qan0vQpmuv7U1lxcXp+4nVIR6Aetb1ACABQAAABwAKWiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACkZVdSrKGUjBBGQaWigDmbjTrzw5O99pCmayY7p7LPT3StvTdTtdVtVuLWTcp4I7qfQirdc/qOiXFrdNqmiMIrnrLB/BOPp2NAEfjb/kH2f/X4n9as3d/dW/idYIoZrmI2RcxRsow2/G7kj6Vy3inxnpVzY21vI0sV7Dcq09sI2ZosZyTgf/XrW/thPEt6W8N7X/d+VLqJyBGuclQD3+vNWtNWiHromTRarqzxXy2tu73L3xhiSUgiBdinJxxj/GtLR9Cj00tczSG5vpeZbh+v0HoKv21pFbeY0agPM++Vh/G2AM/oKnpSabuhxTS1CiiipKCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigApKWigDxXxJ4a1qw1++kbT7q7iurl5op4IzIGDHIBxyCOnPpxXa/DXQ9R0mwvbjUIWtjeSq0cD/eUKuNzDsT6deBXa0V0TxM501TeyMY0Ixm5rdhRRRXObBRRRQAUUUUAFFFFABRRRQAUUUUAf//Z)
⇒ The Rhombus has a property
Diagonal of rhombus bisect each other at 90°
This is conveyed by square
as their diagonal also bisect each other at 90°
∴ A square is a rhombus
(v) [False]
![](data:image/jpeg;base64,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)
⇒ The square has a property
All angles of square are equal and 90°
And diagonals are equal and perpendicular bisector to each
other
Which is not conveyed by Rhombus
as their diagonal are perpendicular bisector but not equal
And their angles are also not equal to 90°
∴ Every rhombus is not a square.
(vi) [False]
![](data:image/jpeg;base64,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)
⇒ The rectangle has a property
Every angle of rectangle is 90°
Which is not conveyed by parallelogram
as it have only opposite side angles are equal not 90°
∴ Every parallelogram are not rectangle.
Question 2.Complete the following table by writing (YES) if the property holds for the particular Quadrilateral and (NO) if property does not holds.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Question 3.ABCD is trapezium in which AB || CD. If AD = BC, show that ∠A = ∠B and ∠C = ∠D.
Answer:![](data:image/jpeg;base64,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Given:- ABCD is a isosceles trapezium
Trapezium with one pair of sides is parallel
And other pair of sides is equal[AD=BC].
Formula used:- SSS congruency property
If all 3 sides of triangle are equal to all 3 sides of
other triangle
Then; Both triangles are congruent
Solution:- In trapezium ABCD
If AB||CD
And; AD=BC
∴ ABCD is a isosceles trapezium
⇒ If ABCD is a isosceles trapezium
Then;
Diagonals of ABCD must be equal
∴ AC=BD
In Δ ABD and Δ ABC
AC=BD [∵ ABCD is isosceles trapezium]
AD=BC [Given]
AB=AB [Common line in both triangle]
∴ Both triangles are congruent by SSS property
∆ABD ≅ ∆ABC
⇒ If both triangles are congruent
Then there were also be equal.
∴ ∠ A=∠ B
As ABCD is trapezium and AB||CD
∠ A+∠ D=180° and ∠ C+∠ B=180°
∠ A =180° - ∠ D and ∠ B=180° - ∠ C
If ∠ A=∠ B;
180° - ∠ D=180° - ∠ C
180° +∠ C - 180° = ∠ D
∴ ∠ C=∠ D;
Conclusion:- If ABCD is trapezium in which AD = BC, then ∠A = ∠B and ∠C = ∠D.
Question 4.The four angles of a quadrilateral are in the ratio 1: 2:3:4. Find the measure of each angle of the quadrilateral.
Answer:![](data:image/jpeg;base64,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)
Given . Angles of a quadrilateral are in the ratio 1: 2:3:4
Solution .
Let any quadrilateral be ABCD
Then
Sum of all angles of quadrilateral is 360°
∴ ∠ A + ∠ B + ∠ C + ∠ D=360°
If angle A,B,C,D are in ratio 1:2:3:4
Then,
1x + 2x + 3x + 4x =360°
10x=360°
x= ![](data:image/png;base64,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)
x= 36°
all angles are 1x,2x,3x,4x
Conclusion.
∴ Angles are 36° , 72° , 108° , 144°
Question 5.ABCD is a rectangle AC is diagonal. Find the angles of ∆ACD. Give reasons.
Answer:![](data:image/jpeg;base64,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)
Given:- ABCD is a rectangle
Formula used:- All angles of rectangle are 90°
In right angle triangle
Pythagoras theorem a2+b2=c2
Sin(θ)=![](data:image/png;base64,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)
Solution:-
In ΔACD
∠ D=90° [All angles of rectangle are 90° ]
∠ ACD=θ1
And; Sin(θ1) =
=![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAfCAMAAADdjm27AAAAAXNSR0IArs4c6QAAAGZQTFRFAAAA///b//+22///tv///9u2/9uQ29uQttu2kNv//7Zm27aQZrb/Zrbb25Bm25A6ZpC2OpDbOpC2tmY6tmYAOma2kDpmAGa2kDoAZjoAOjo6ADqQADo6ZgAAOgAAAABmAAA6AAAAjTcC/gAAAAF0Uk5TAEDm2GYAAACkSURBVHjatZDLEoMgEARHEfLSGKNGDYLO//9kCkRCVS65OBfYZplDA/8mNwMAZUmuvfDo+l4KdywFblY7lr3OpgwIyvprj27YUTY2ANrLNgU0hFqW6VbdhLfYJX11u26/5aQFRrqJ1CdXMD8Ejg5/guOzuQfkRK5V6l7Zp8g6JzW673S0ENznpolVwX2CdvcJ2t17/376uq9ZQbrV6F7gbsm5wgcfBhCROsg+MgAAAABJRU5ErkJggg==)
θ1=arc sin(
)
∠ DAC=θ2
And; Sin(θ2) =
=![](data:image/png;base64,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)
θ1=arc sin(
)
Conclusion:-
The angles of Δ ACD are :-
∠ D=90°
∠ DAC=arc sin(
)
∠ ACD=arc sin(
)
State whether the statements are True or False.
(i) Every parallelogram is a trapezium ( )
(ii) All parallelograms are quadrilaterals ( )
(iii) All trapeziums are parallelograms ( )
(iv) A square is a rhombus ( )
(v) Every rhombus is a square ( )
(vi) All parallelograms are rectangles ( )
Answer:
(i) [True]
⇒ The trapezium has a property
One pair of opposite sides are parallel
This is conveyed by parallelogram
as they have 2 pair of parallel sides
∴ Every parallelogram is a trapezium
(ii) [True]
⇒ The quadrilateral is known as
Polygon having four sides
This is conveyed by parallelogram
as they are also four sided polygon.
∴ Every parallelogram is a Quadrilateral
(iii) [False]
⇒ The parallelogram has a property
Both pair of opposite sides are parallel and equal
Which is not conveyed by trapezium
as they have only 1 pair of parallel sides
∴ Every trapezium is not parallelogram
(iv) [True]
⇒ The Rhombus has a property
Diagonal of rhombus bisect each other at 90°
This is conveyed by square
as their diagonal also bisect each other at 90°
∴ A square is a rhombus
(v) [False]
⇒ The square has a property
All angles of square are equal and 90°
And diagonals are equal and perpendicular bisector to each
other
Which is not conveyed by Rhombus
as their diagonal are perpendicular bisector but not equal
And their angles are also not equal to 90°
∴ Every rhombus is not a square.
(vi) [False]
⇒ The rectangle has a property
Every angle of rectangle is 90°
Which is not conveyed by parallelogram
as it have only opposite side angles are equal not 90°
∴ Every parallelogram are not rectangle.
Question 2.
Complete the following table by writing (YES) if the property holds for the particular Quadrilateral and (NO) if property does not holds.
Answer:
Question 3.
ABCD is trapezium in which AB || CD. If AD = BC, show that ∠A = ∠B and ∠C = ∠D.
Answer:
Given:- ABCD is a isosceles trapezium
Trapezium with one pair of sides is parallel
And other pair of sides is equal[AD=BC].
Formula used:- SSS congruency property
If all 3 sides of triangle are equal to all 3 sides of
other triangle
Then; Both triangles are congruent
Solution:- In trapezium ABCD
If AB||CD
And; AD=BC
∴ ABCD is a isosceles trapezium
⇒ If ABCD is a isosceles trapezium
Then;
Diagonals of ABCD must be equal
∴ AC=BD
In Δ ABD and Δ ABC
AC=BD [∵ ABCD is isosceles trapezium]
AD=BC [Given]
AB=AB [Common line in both triangle]
∴ Both triangles are congruent by SSS property
∆ABD ≅ ∆ABC
⇒ If both triangles are congruent
Then there were also be equal.
∴ ∠ A=∠ B
As ABCD is trapezium and AB||CD
∠ A+∠ D=180° and ∠ C+∠ B=180°
∠ A =180° - ∠ D and ∠ B=180° - ∠ C
If ∠ A=∠ B;
180° - ∠ D=180° - ∠ C
180° +∠ C - 180° = ∠ D
∴ ∠ C=∠ D;
Conclusion:- If ABCD is trapezium in which AD = BC, then ∠A = ∠B and ∠C = ∠D.
Question 4.
The four angles of a quadrilateral are in the ratio 1: 2:3:4. Find the measure of each angle of the quadrilateral.
Answer:
Given . Angles of a quadrilateral are in the ratio 1: 2:3:4
Solution .
Let any quadrilateral be ABCD
Then
Sum of all angles of quadrilateral is 360°
∴ ∠ A + ∠ B + ∠ C + ∠ D=360°
If angle A,B,C,D are in ratio 1:2:3:4
Then,
1x + 2x + 3x + 4x =360°
10x=360°
x=
x= 36°
all angles are 1x,2x,3x,4x
Conclusion.
∴ Angles are 36° , 72° , 108° , 144°
Question 5.
ABCD is a rectangle AC is diagonal. Find the angles of ∆ACD. Give reasons.
Answer:
Given:- ABCD is a rectangle
Formula used:- All angles of rectangle are 90°
In right angle triangle
Pythagoras theorem a2+b2=c2
Sin(θ)=
Solution:-
In ΔACD
∠ D=90° [All angles of rectangle are 90° ]
∠ ACD=θ1
And; Sin(θ1) = =
θ1=arc sin()
∠ DAC=θ2
And; Sin(θ2) = =
θ1=arc sin()
Conclusion:-
The angles of Δ ACD are :-
∠ D=90°
∠ DAC=arc sin()
∠ ACD=arc sin()
Exercise 8.2
Question 1.In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD ≅ ∆BEC.
![](data:image/png;base64,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)
Answer:Given :- ABCD is a parallelogram and ABEF is a rectangle
Formula used :-
SAS congruency rule
If two sides of triangle and angle made by the 2 sides are equal then both the triangles are congruent
Solution :-
In ∆AFD and ∆BEC
*AF=BE [opposite sides of rectangle are equal]
*AD=BC [opposite sides of parallelogram are equal]
As angle of rectangle is 90°
∠ DAB +∠ FAD=90°
∠ DAB=90° - ∠ FAD -----1
Sum of corresponding angles of parallelogram is 180°
∠ DAB+∠ ABC =180°
∠ DAB+∠ ABE+∠ EBC=180°
90° - ∠ FAD + 90° +∠ EBC=180° ∵ putting value from 1
180° +∠ EBC-∠ FAD=180°
∠ EBC - ∠ FAD=0
∠ EBC = ∠ FAD
⇒ Hence;
By SAS property both triangles are congruent
Conclusion :-
∆AFD ≅ ∆BEC
Question 2.Show that the diagonals of a rhombus divide it into four congruent triangles.
Answer:![](data:image/jpeg;base64,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)
Given :- ABCD is a rhombus
Formula used :-
*SSS congruency rule
If all sides of both triangles are equal then both triangles are congruent
*properties of rhombus
Solution :-
In Δ AOD and Δ COB
AO=OC [diagonal of Rhombus bisect each other]
OD=OB [diagonal of Rhombus bisect each other]
AD=BC [all sides of rhombus are equal]
∴ Δ AOD ≅ Δ COB
In Δ AOB and Δ COD
AO=OC [diagonal of Rhombus bisect each other]
OD=OB [diagonal of Rhombus bisect each other]
CD=BA [all sides of rhombus are equal]
∴ Δ AOB ≅ Δ COD
In Δ AOB and Δ AOD
AO=AO [Common in both triangles]
OD=OB [diagonal of Rhombus bisect each other]
AD=AB [all sides of rhombus are equal]
∴ Δ AOB ≅ Δ AOD
∴ All four triangles divide by diagonals of triangle are congruent
Question 3.In a quadrilateral ABCD, the bisector of ∠C and ∠D intersect at O.
Prove that ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMkAAAA1CAYAAADrls9nAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAVXSURBVHja7Vw9btswFOYBeoAWMLvlAA6dKzhCUKBrHSFTg04FgaJzoGQzUOQC2bq1Q+cO7dqlN8iQG/QObSmFEq3w51GkbDn5hm8xTInv53vvkY8Uu7q6YgAAuAElAABIAgAgCQCAJAAAkgAASPK0IeVqvlyKC87ZLV++/widgCSAgctSvGKc3yqCMMb+giQgCeAjC0gCkgAgCUgCgCQgCQCSACAJSAKAJCAJAJKAJABIApIAIAlIEjW2ksW8KOUJ9JgfsixOClnNQZI9JokaJ5byHDocD6eCX4vy8hVIMhGSMHH6OSaDcF58fbdeP4MOx8N6/e5ZwflXV0ZJfkFjyMX3s6p6sfn76uBYvLzhjP2pnUNF0f//W0k5V2OEKCtnCpSr+YLz73qcHtsvOWrhZuyn+b8HUOemFosvuypXav0YOmjlCWQULZsvwuWyVRdR2Wc2K37uAym1LKtKHpB8QJxeS3n53BvEHLJncAB+axpSGVelr9oRehNTzn/I2W9XRO3G8j9HRflBT1j9XhZHH2pnswhSVWcvmueKu5WsDsznyfLojT5cyPjhb5eDTDLzZHRYm636OhSM3Sndh2r0SRCkJ4vpA6aNL6V8rv3RJ5uW36af7Eqvo5EnUrbR30ISPdZlyLZk6TlPl1E2FWTNOHsQKX06GoMgCu+X/CM1y02NIBQfaOXz2N+VSQdHOTXRPitdTkyptVshAo5hI2FIQZuRcvrbsLpEy1FquWxlLe3Ozs5rHWUIJMqeufXskyXkA13Z6/aRxn8fZptsEzWjdci46r9LsbwwyynqWBsRKSTZjJb+/+0azTzTyx4KQfpBqwlC6e/OTZKQLCEfoARwTaT+vKMmqup7lwJTatqO5eGxtv9SSRLznl2icdQ0IvtsZXufdowhu3Bjk4Qii88H6nXpvd19Qbj1j57skRPdXBjncsDWMFEk6bIOmSRGyeVSllmbhzBG2UaVJcVWDzY92OEP/S5KWbJNklBlCe90irugb2n/6GWbiPTvn2iKcqdEkp2vRxyGiivVaARp/29EzpjSd2ySxMji8oF2h/PeZ9SOa9g/Np9Bmyhh6zQlk6DcssxxAEmotiJHX2LJFZN9qcQbLkto4e6eQ/eMTf/INtGUCGSODUWfLAv3kbeBqQ5jIpUksU7V6tLWd8pQcqVkkiGyUHxA74y6yB9NkroBM8RQxAhUFsVbUxiqA9t6KTm3gHe9JhlCkiG20rq0BbQcJddQkgyVZaskabveSRP1O5BcinN3M4jQTOwJ+Ziaia662KXvobZqyOiO1qm7XLEkSZGFVG4RgqTrGZaJpp3f6Y4HsL8vxfGNuejSRwTCk/wvSFFWtmMpauEVdyylODHnszfd9gBJUmzVvmNRfAv1DJTejkr5ZkyS5PW7hwt90we8fZLQ7hbpsGBE2aEmZjukSNmpcI+V87htv+ZwW5+sU0eooZdiq9nx67WOqK4dxW63MX4RH0uSVL+jjp/NZr8U2b0nQTRJhvZJgO0hV8cdGLYeTOq4A9s11lR7OY8V2c5uAVtcl2Q6BQxElLm5TgEDsZlhddAuHO/vtYQugTVRbdoHMR9jYMp6nwSIK51iu89j3EwEAkFpjJuJAC06mdvZKqt0uzGEYzS4474dO415xx3wZxHbl05cnV3nMzzfAwDSYWtugyRTWSQS1xz47taIBMF3t6ZdhmH3aj8AJexsMb8/X24BSaCEHZRa/i8GAiDJk8YYXxEBQJJHA3zXFyQBAusQbOWCJIAng9g+QKAai0IUn9AsBEmeNMwvdWzrCjAAkuwVQfyXgXBnBCQBAJAEAEASAHjy+AdgR7ieXpGqmAAAAABJRU5ErkJggg==)
Answer:![](data:image/jpeg;base64,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)
Given :- ABCD is a quadrilateral
∠ OCB= ∠ OCD=∠C/2 [OC is bisector of ∠ C]
∠ ODA= ∠ ODC=∠D/2 [OD is bisector of ∠ D]
Formula Used:- ∠ A+ ∠ B+∠ C+ ∠ D=360°
Solution :-
In Δ COD
∠ OCD+ ∠ COD +∠ ODC=180°
∠D/2 + ∠C/2 +∠ COD = 180°
(∠ D+∠ C)/2 + ∠ COD = 180°
If;
∠ A+ ∠ B+∠ C+ ∠ D=360°
∠ C+ ∠ D=360° -(∠ A+ ∠ B)
+ ∠ COD=180°
180° -
+ ∠ COD=180°
∠ COD=![](data:image/png;base64,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)
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD ≅ ∆BEC.
Answer:
Given :- ABCD is a parallelogram and ABEF is a rectangle
Formula used :-
SAS congruency rule
If two sides of triangle and angle made by the 2 sides are equal then both the triangles are congruent
Solution :-
In ∆AFD and ∆BEC
*AF=BE [opposite sides of rectangle are equal]
*AD=BC [opposite sides of parallelogram are equal]
As angle of rectangle is 90°
∠ DAB +∠ FAD=90°
∠ DAB=90° - ∠ FAD -----1
Sum of corresponding angles of parallelogram is 180°
∠ DAB+∠ ABC =180°
∠ DAB+∠ ABE+∠ EBC=180°
90° - ∠ FAD + 90° +∠ EBC=180° ∵ putting value from 1
180° +∠ EBC-∠ FAD=180°
∠ EBC - ∠ FAD=0
∠ EBC = ∠ FAD
⇒ Hence;
By SAS property both triangles are congruent
Conclusion :-
∆AFD ≅ ∆BEC
Question 2.
Show that the diagonals of a rhombus divide it into four congruent triangles.
Answer:
Given :- ABCD is a rhombus
Formula used :-
*SSS congruency rule
If all sides of both triangles are equal then both triangles are congruent
*properties of rhombus
Solution :-
In Δ AOD and Δ COB
AO=OC [diagonal of Rhombus bisect each other]
OD=OB [diagonal of Rhombus bisect each other]
AD=BC [all sides of rhombus are equal]
∴ Δ AOD ≅ Δ COB
In Δ AOB and Δ COD
AO=OC [diagonal of Rhombus bisect each other]
OD=OB [diagonal of Rhombus bisect each other]
CD=BA [all sides of rhombus are equal]
∴ Δ AOB ≅ Δ COD
In Δ AOB and Δ AOD
AO=AO [Common in both triangles]
OD=OB [diagonal of Rhombus bisect each other]
AD=AB [all sides of rhombus are equal]
∴ Δ AOB ≅ Δ AOD
∴ All four triangles divide by diagonals of triangle are congruent
Question 3.
In a quadrilateral ABCD, the bisector of ∠C and ∠D intersect at O.
Prove that
Answer:
Given :- ABCD is a quadrilateral
∠ OCB= ∠ OCD=∠C/2 [OC is bisector of ∠ C]
∠ ODA= ∠ ODC=∠D/2 [OD is bisector of ∠ D]
Formula Used:- ∠ A+ ∠ B+∠ C+ ∠ D=360°
Solution :-
In Δ COD
∠ OCD+ ∠ COD +∠ ODC=180°
∠D/2 + ∠C/2 +∠ COD = 180°
(∠ D+∠ C)/2 + ∠ COD = 180°
If;
∠ A+ ∠ B+∠ C+ ∠ D=360°
∠ C+ ∠ D=360° -(∠ A+ ∠ B)
+ ∠ COD=180°
180° - + ∠ COD=180°
∠ COD=
Exercise 8.3
Question 1.The opposite angles of a parallelogram are
and
Find the measure of each angle of the parallelogram.
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACFAOkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiikoAWiub+33vmXPl3Esl0l6Y47Yxja0eR7ZAxk7s9q6OqlFxJjK4tFFFSUFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRWPrF3qHnpa6ZHIZEXzZHCAj/AGU5/vHOe4ApxV3YTdkbFFQWVyLy0iuFRo965KOMFT3B+h4qelsPcKKKKACiiigAooooAK8h1nxz4og1u5ge4/s9opWVLUQK3y5+U8glsjByOOeK9ZuLiO1t5LiZtscalmPsKyPDls80c2sXSf6RfNvUEcpH/Co/DmtaU4wd5RuZ1IOSsnYj0jV9fu9Jtri70HZPJGC6+eqc/wC6eRnrg9Kufb9X/wCgJ/5NJWnS1kaGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAHmXjLxf4l07VVtRH/AGTblAY2wshmPf5yCOOmBz3710ngPWdW1vSJZtVj+5Lthn8vZ5y4GTj2ORkcGrNkBrfiCa/cb7SxzDbg8hn/AIm/pW/WrqRdNR5de5moNTcr6dgpaKKyNAooooAKKKKACiiorm4jtLaS4mbbHEpZj7CgDF11jqeoW2hRk7HPnXRHaMHgfia3lUKoVQAAMADtWL4bt5Hhm1a6XFxftvwf4I/4V/KtugAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACsnxFfyWeniG25u7thDAB6nqfwFa1c/p/8AxOfEE+pH5rayzBbejN/G39KANXTLCPTNOhs4uREuCf7x7n86t0UUAFFFFABRRRQAUUUUAFYGuE6pqVtocZPlt++uyO0YPC/ia2bq5is7WW5mbbHEpZj7Csvw3bStBNql0uLm/bzCD/An8K/lQBsgBQFUAADAA7UtFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAZPiK+ktdPEFtzd3jeTAB6nqfwFXNNsY9N0+Gzi+7EuM+p7n86ydO/4nGvz6o3NtaZt7b0Lfxt/SugoAKKKKACiiigAooooAKKKhu7qKytJbqZtscSlmP0oAxtbJ1XVLbQ4z+74nuyOyA8L+JreACgADAHQCsbw3ay/Z5dTulxc37eYwP8ACn8K/lW1QAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABWR4jvpLawW2tf8Aj7vG8mEemep/AVr1z+mf8TjXrjVW5t7XNva+hP8AG39KANfTrGPTrCGzh+7EuM+p7n86s0UUAFFFFABRRRQAUUUUAFYGtE6rqttoiHMS4nuyP7g+6v4mti8uorGzlupjiOJSzVmeG7WUWsupXS4ur9vNfP8ACv8ACv4CgDZAAAAGAOlLRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGR4jvZYLFbS1/4+71vJi9s9W/AVe0+yi06whtIR8kShc+vqayNL/4nGuXGrtzb2+be19/7zf0roKACiiigAooooAKKKKACiio7iXyLeSXaz7FLbVGSfYUAYesn+1tXttFQ5hTFxd4/uj7q/ia3wMDA4FY3hq2dbaa+uGVru8kMkoDA7P7q8egraoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArH8R3ksNklnan/AEu+byYvYH7zfgK1ycDJ4ArD06J9Q8QXOpzABLceRarkHj+J/wAaANWws4tPsYbSEYSJQo9/U1YoooAKKKKACiiigAooooAQkDk9KwtSvV1e4l0axeOU+UJZZA+VXDAhGx2YAg/Wk8Z6Lfa94feysLgRS+YrsjMVWZR1QkdAev4VxvhjwH4hstahvJJE0pIs7midXaQEH5cDjHfn04raEY8rnzWa6GU5S5lG2j6noVlbyLdSTvZQW25An7tss2M9cADHPFX6yv7L1H/oOXH/AH5j/wAKP7L1H/oOXH/fmP8AwrJu5olY1aKyv7L1H/oOXH/fmP8Awo/svUf+g5cf9+Y/8KQzVorK/svUf+g5cf8AfmP/AAo/svUf+g5cf9+Y/wDCgDVorK/svUf+g5cf9+Y/8KP7L1H/AKDlx/35j/woA1aKyv7L1H/oOXH/AH5j/wAKP7L1H/oOXH/fmP8AwoA1aKyv7L1H/oOXH/fmP/Cj+y9R/wCg5cf9+Y/8KANWisr+y9R/6Dlx/wB+Y/8ACj+y9R/6Dlx/35j/AMKANWisr+y9R/6Dlx/35j/wo/svUf8AoOXH/fmP/CgDVorK/svUf+g5cf8AfmP/AAqG90XVbixngi8Q3MUkkbKriJPlJHB4GaAJ9U1K1Vk00So1zebolQNkr8p5I646VV0bSLqyureaYIoitfIYbgxJ46YAwOD1z2rzuD4beJReIixW9syuCLxZ87SD94fxE/XHvXsKghQCckDk+tdFRRpq0ZXuYwvN3krWFooornNgooooAKKKKACimsdoJpv7z2oAkooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAGuMqar+ZJ/e/SiigD/9k=)
Given:- Opposite angles of parallelogram
and ![](data:image/png;base64,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)
Formula used:- opposite angles of a parallelogram are equal
Corresponding angles sum is 180°
Solution:-
Let ∠ A and ∠ C
∠ A = ∠ C [opposite angles of a parallelogram are equal]
3x-2=x+48
3x – x=48+2
2x=50
x=25
Then;
∠ A=∠ C=x+48=25+ 48 = 73°
∠ A+∠ B=180°
∠ B=180° - 73°
∠ B= 107°
∠ B = ∠ D [opposite angles of a parallelogram are equal]
Conclusion:-
Angles of parallelogram = 73°, 107°, 73°, 107°
Question 2.Find the measure of all the angles of a parallelogram, if one angle is 24° less than the twice of the smallest angle.
Answer:![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACFAOkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiikoAWiub+33vmXPl3Esl0l6Y47Yxja0eR7ZAxk7s9q6OqlFxJjK4tFFFSUFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRWPrF3qHnpa6ZHIZEXzZHCAj/AGU5/vHOe4ApxV3YTdkbFFQWVyLy0iuFRo965KOMFT3B+h4qelsPcKKKKACiiigAooooAK8h1nxz4og1u5ge4/s9opWVLUQK3y5+U8glsjByOOeK9ZuLiO1t5LiZtscalmPsKyPDls80c2sXSf6RfNvUEcpH/Co/DmtaU4wd5RuZ1IOSsnYj0jV9fu9Jtri70HZPJGC6+eqc/wC6eRnrg9Kufb9X/wCgJ/5NJWnS1kaGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAGX9v1f/oCf+TSUfb9X/6An/k0lalFAGX9v1f/AKAn/k0lH2/V/wDoCf8Ak0lalFAHmXjLxf4l07VVtRH/AGTblAY2wshmPf5yCOOmBz3710ngPWdW1vSJZtVj+5Lthn8vZ5y4GTj2ORkcGrNkBrfiCa/cb7SxzDbg8hn/AIm/pW/WrqRdNR5de5moNTcr6dgpaKKyNAooooAKKKKACiiorm4jtLaS4mbbHEpZj7CgDF11jqeoW2hRk7HPnXRHaMHgfia3lUKoVQAAMADtWL4bt5Hhm1a6XFxftvwf4I/4V/KtugAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACsnxFfyWeniG25u7thDAB6nqfwFa1c/p/8AxOfEE+pH5rayzBbejN/G39KANXTLCPTNOhs4uREuCf7x7n86t0UUAFFFFABRRRQAUUUUAFYGuE6pqVtocZPlt++uyO0YPC/ia2bq5is7WW5mbbHEpZj7Csvw3bStBNql0uLm/bzCD/An8K/lQBsgBQFUAADAA7UtFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAZPiK+ktdPEFtzd3jeTAB6nqfwFXNNsY9N0+Gzi+7EuM+p7n86ydO/4nGvz6o3NtaZt7b0Lfxt/SugoAKKKKACiiigAooooAKKKhu7qKytJbqZtscSlmP0oAxtbJ1XVLbQ4z+74nuyOyA8L+JreACgADAHQCsbw3ay/Z5dTulxc37eYwP8ACn8K/lW1QAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABWR4jvpLawW2tf8Aj7vG8mEemep/AVr1z+mf8TjXrjVW5t7XNva+hP8AG39KANfTrGPTrCGzh+7EuM+p7n86s0UUAFFFFABRRRQAUUUUAFYGtE6rqttoiHMS4nuyP7g+6v4mti8uorGzlupjiOJSzVmeG7WUWsupXS4ur9vNfP8ACv8ACv4CgDZAAAAGAOlLRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGR4jvZYLFbS1/4+71vJi9s9W/AVe0+yi06whtIR8kShc+vqayNL/4nGuXGrtzb2+be19/7zf0roKACiiigAooooAKKKKACiio7iXyLeSXaz7FLbVGSfYUAYesn+1tXttFQ5hTFxd4/uj7q/ia3wMDA4FY3hq2dbaa+uGVru8kMkoDA7P7q8egraoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArH8R3ksNklnan/AEu+byYvYH7zfgK1ycDJ4ArD06J9Q8QXOpzABLceRarkHj+J/wAaANWws4tPsYbSEYSJQo9/U1YoooAKKKKACiiigAooooAQkDk9KwtSvV1e4l0axeOU+UJZZA+VXDAhGx2YAg/Wk8Z6Lfa94feysLgRS+YrsjMVWZR1QkdAev4VxvhjwH4hstahvJJE0pIs7midXaQEH5cDjHfn04raEY8rnzWa6GU5S5lG2j6noVlbyLdSTvZQW25An7tss2M9cADHPFX6yv7L1H/oOXH/AH5j/wAKP7L1H/oOXH/fmP8AwrJu5olY1aKyv7L1H/oOXH/fmP8Awo/svUf+g5cf9+Y/8KQzVorK/svUf+g5cf8AfmP/AAo/svUf+g5cf9+Y/wDCgDVorK/svUf+g5cf9+Y/8KP7L1H/AKDlx/35j/woA1aKyv7L1H/oOXH/AH5j/wAKP7L1H/oOXH/fmP8AwoA1aKyv7L1H/oOXH/fmP/Cj+y9R/wCg5cf9+Y/8KANWisr+y9R/6Dlx/wB+Y/8ACj+y9R/6Dlx/35j/AMKANWisr+y9R/6Dlx/35j/wo/svUf8AoOXH/fmP/CgDVorK/svUf+g5cf8AfmP/AAqG90XVbixngi8Q3MUkkbKriJPlJHB4GaAJ9U1K1Vk00So1zebolQNkr8p5I646VV0bSLqyureaYIoitfIYbgxJ46YAwOD1z2rzuD4beJReIixW9syuCLxZ87SD94fxE/XHvXsKghQCckDk+tdFRRpq0ZXuYwvN3krWFooornNgooooAKKKKACimsdoJpv7z2oAkooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAGuMqar+ZJ/e/SiigD/9k=)
Given:- one angle is 24° less than the twice of the smallest angle
Formula used:- opposite angles of a parallelogram are equal
Corresponding angles sum is 180°
Solution:-
Let ∠ A and ∠ C be smallest because
∠ A = ∠ C [opposite angles of a parallelogram are equal]
2∠ A+ 24° =∠ B
∠ A+∠ B=180° [Sum of corresponding angles is 180° ]
∠ B=180°-∠ A
Then,
2∠ A+ 24° =180° -∠ A
3∠ A =180° - 24°
3∠ A=156°
∠ A=
=52°
∠ B=180° -∠ A
∠ B= 180° -52°
∠ B=128°
∠ B = ∠ D [opposite angles of a parallelogram are equal]
Conclusion:-
∴ Angles of parallelogram = 52°, 128°, 52°, 128°
Question 3.In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB.
![](data:image/jpeg;base64,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)
Answer:Given :- ABCD is a parallelogram
And CE=EB
Formula used:- ASA congruency property
If 2 angles and one side between them in two
triangles are equal then both triangle are congruent
Solutions :-
In Δ DCE and Δ FBE
∠ DEC=∠ BEF [Vertically opposite angles]
As DC || BF
∠ ECD=∠ EBF [Alternate angles]
And;
CE=EB [Given]
∴ Δ DCE ≅ Δ FBE
As Δ DCE ≅ Δ FBE
Then
DC=BF
And DC=AB [opposite sides of parallelogram are equal]
Hence ;
AB=BF
AF=AB+BF
AF=2AB.
Hence Proved;
Question 4.In the adjacent figure ABCD is a parallelogram P, Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.
![](data:image/png;base64,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)
Answer:Given:-ABCD is a parallelogram
P,Q are the midpoints of sides AB and DC respectively.
Solution:-
In parallelogram ABCD
If P,Q are the midpoints of sides AB and DC respectively
∴ DC=2QC=2QD
∴ AB=2AP=2PB
If DC||AB
Then;
QD||AP and QC||PB
Line PQ divides the parallelogram in 2 equal parts
Because P and Q are midpoints
∴ AD||PQ||CB
If;
PQ||CB and QC||PB
Then, PBCQ is also a parallelogram
Question 5.ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD || BA as shown in the figure. Show that
(i) ∠DAC = ∠BCA
(ii) ABCD is a parallelogram
![](data:image/jpeg;base64,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)
Answer:Given:- AB=AC and ABC is isosceles triangle
∠ QAD=∠ DAC
CD||BA
Formula used:- sum of angles of triangle is 180°
Solution:-
As Δ ABC is a isosceles triangle
∠ ABC=∠ ACB
∠ ABC+∠ ACB+∠ CAB=180°
2∠ ACB+∠ CAB=180°
*As BAQ is a straight line
∠ CAB+∠ DAC+∠ QAD=180°
*∠ QAD=∠ DAC [Given]
∠ CAB=180° - 2∠ DAC
Putting value of ∠ CAB in above equation 1
2∠ ACB+180° - 2∠ DAC=180°
2∠ ACB =2∠ DAC
∠ ACB =∠ DAC
If;
There is ∠ ACB =∠ DAC and AC is the transverse
∴ these are equal by alternate angles
And AD||BC
In ABCD
If;
AD||BC & CD||BA
If both pair of sides of quadrilateral are parallel
Then the quadrilateral is parallelogram
Conclusion:-
ABCD is a parallelogram
And ∠DAC = ∠BCA
Question 6.ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that
(i) Δ APB ≅ Δ CQD
(ii) AP = CQ
![](data:image/png;base64,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)
Answer:Given:- ABCD is parallelogram
Formula used :- AAS property
If 2 angles and any one side is are equal in both triangle
Then both triangles are congruent
Solution:-
In Δ APB and Δ CQD
∠ CQD=∠ APB=90°
If ABCD is a parallelogram
∠ CDB=∠ DBA [alternate angles as DC||AB]
AB=DC [opposite sides of parallelogram are equal]
By AAS property
∴ Δ APB ≅ Δ CQD
If Δ APB ≅ Δ CQD
Then
AP=CQ
Conclusion:-
In parallelogram ABCD; Δ APB ≅ Δ CQD
Question 7.In
and DEF, AB || DE, AB=DE; BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that
(i) ABED is a parallelogram
(ii) BCFE is a parallelogram
(iii) AC = DF
(iv) ∆ABC ≅ ∆DEF
![](data:image/jpeg;base64,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)
Answer:Given:- AB||DE , AB=DE; BC||EF, BC=EF
Formula used:- SSS congruency rule
If all 3 sides of both triangle are equal then
Both triangles are congruent.
Solution:-
(1) In ABED
AB||DE
AB=DE
∴ ABED is a parallelogram
∵ If one pair of side in quadrilateral is equal and parallel
Then the quadrilateral is parallelogram.
(2) In BCFE
BC||EF
BC=EF
∴ BCEF is a parallelogram
∵ If one pair of side in quadrilateral is equal and parallel
Then the quadrilateral is parallelogram.
(3) As ABED is a parallelogram
BE||AD , BE=AD ;
As BCFE is a parallelogram
BE||CF , BE=CF ;
∴ By concluding both above statements
AD||CF and AD=CF
∴ ACFD is a parallelogram
∵ If one pair of side in quadrilateral is equal and parallel
Then the quadrilateral is parallelogram
If ACDF is a parallelogram ;
Then
AC=DF [opposite sides of parallelogram are equal ]
(4) In Δ ABC and Δ DEF
AB=DE [Given]
BC=EF [Given]
AC=DF [Proved above]
Δ ABC ≅ Δ DEF [SSS congruency rule]
Question 8.ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ || AP and also AC bisects PQ (see figure).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMoAAABvCAAAAACI3wApAAAABGdBTUEAALGOfPtRkwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAu4SURBVHja7Zz5kxTVHcD5OwbCsQLLVZHEFFlLUqkosJIoglKkNFmuKjQmlVBiOEoMBDQJAiUYIyhGV2MJSIEaoogRZHeBhc3uzC57zdX3NT3dc0/PsXN0Z6anZ5me6e7ptzMiY+33h+l+08d7n37f7/d93/f1zBTpOyNTJlEmUe4Qipf1eqjkdwGFO7Rh0x927dr/Idn4vXLY0nTo7LEn5z5ha3iUnqaH8pvXZ7bYGx2l954V+U36EctfG6b5ovXEiS4h6YDSwUulvXLPMnl7dPbPkQYhsbWtfbn9wC83Hj34VNurGigXFv/Y2iAky1Z8JUj+va27nlt+JKGBcnbR0sGGIMmumXpO3vnkmd9fVpu9grLvexsiDYHyyYJH6cJe+0dqs+8rmL3QOu1cY+jX89NfKC2WoNyY+WDeJ2xv2hDNF1NOl8vldrtd+uKGYKPDdZTb7cjtuZ1INt/CdZYT2ijCVsv0ve/sXblwq0cus32D13u5u6wjhOG+3hvd13rC+cJTloPaKP7jL+7Zf/DwG+cThTLjlRKYx/jOAeJOs3BDfda+nhF5f/+M9VFtBSsTLB9Z+u2YgS88tGvHS+czd8BVRVmi8FDTTjvmGOiF5MLQDxd+Le+Qp84FjFDQbGFjZ3VOOPHAlvf+82LLlrFvmkR0kvyY0idQRIRwVBnC987+FSJK4s3jH518c0g0QCnuQCOaFvPBnI35zamZm76R9o/BbrudUn1FjzpyKhCwS9li2/7y/aW/Ofj81u7cuP67nboo8ZJYn3D4K46H1jSdyW+jD07/pK4IvLJTNrZlMce4eoyNm+josT3HO+TGeb7URWGDJYUk7CofNU/PebQA+8L0p+P14ohACMNrHYiSkO92iS/RebG62cNqEwjaUbV9/83yrGIyc1fW6scy0bCyJ4iaPYU4faVlUtA6SxfFVdFNIypn9nIRpb15FV0TiMcFE16D40nEVdZT2l5VF8VZ+RUxAt8uHJ+2Cpd3Xpm1OTYBgBjtwMyc57W7YhVsYChurS/x2565d+miC/LO+hntEyAhaSFV/aw0ai9tNl/wXFHAXuG1v6bckXFj2S0j3/t4yGz7eZomAVxEHB9UjWmCrVB3iAZCSeg9s4yHThf2dj/0rjfRv+PJkeoPt9iWBEC/xUmYUzuBAcU5cBwQCq9fR4RQDh5/dsv61m3V3FeMo2nwgCDprhjLmCIB4wdCQY3qiUAFjxPbuei+03onJaSJi9/hDlR8Oa4nVBQIBTKuKwzLjl58Z+nqfi33ANGeic9EQ07Y8DguAaFUzbn4EUHKJMi+Uwfbi9ixIM1INQuDhaoZERiKiWxrhHC5c00fvKQ8Q18wma2VI+VlotXO8XmBULJRE/W6EAzxSXWUrIcyoZZ0EAjF1PiNQggMuem6kXgxvQdIlLpAIgaEwpqpmsRJhnRT9eEIQfp2RqksF00DoZgJjzKovBEwb+0gHGqQEPGrQ1s996aDAhS2B1B9n8PerB4M5JyWkULHyhYWHEAoKQ/YQ2VJ7dUy8u/7jry0/3ODK8WAl8ZDQJXhQCjhAKCCJHAt6+9ft+FL6ua+Zcf0Lkty9q6rTkCj8gOhRFISqMSQCrONP7JE1uvdze9pXjLG3+rosoUAK8IjQCgTmUtJgrtsXG2fu1Xeftn8WFBLK29c7kTHRNBqkDQQSlX9Cmt3JlpqY+mNc07KO9jKBR+Xn5q2d3f0EBOJ01wSCIpQzb1ieilJf0nUGnh4/vXC7dbPfrtc4W912fBw1WanNbRvFAgl4DeuARX0j9FUahyl+b8KSvO/1NaOQ7DHTIJ2SCMucgKh8MazVsIwv59W0rtSevOs1wuG2vqDrlJrH+l1mHvTYZCsWcGqxIhClRbElRikffYm2ai/aH6y5N62bodgCkSCtRbdozAQil+qUZKyM0utu/dabiNuu3d8kPQM32IEs1MBzc4P+oFQQlLNEiFzXRt4+vG3ey7uePRM4TuRwflwtMYb4yIISrIuOWAOy0pc+58P/+O1m3I54/dEsrXf1iGBoHjTUl2Ezk0VBHshMs3SeLQuN3UBodRtVS6J8bmPXOiQxtF6LSiBoehPVljQF6ySJEfjFAQ808R0VRECQtGtODkC2iQp6kQQF/DcjBjQbQIKhOIHNzk9yRBuFIUAZz9SfEDfmdAgKCk9B5YETThmgt5QEHF7fV6wK2F9v2MwTdNACQDH3dqSJbD8Q0nngxQSJJmRNvB1uASCUh8HFkFwleniaD3umkGBUOA6VOmBKuK4dM5san5fNokAoUA1PzqG0jQ3f+d1vMZbxwkgFKy22rKc7uw7YOu01vbqb4gBQtGaDZueuWZoImhw2HW1c5QzisSquBzWC4Kipc8BkyODSGFVzCEFd1x26Hsob5VIlgyCoGjMEoLmnBoH8SbOEpydV0Z1IjKm2vtneBYEpdIyE6aSbhxqMg+YDQx8dR3TGgX5awMcx0T1lSxl5Dam1MfqxzwcwIA+Rg929GhkbUJDb67fsP2Pe87rWj0NhDIRF+Mz0mFNo4L+1zlAV8K0WxaeOd8666hez/MgKDEWlCONYgI4vQh3XRnxl6t+/7xVknRp1gM6Ks2EQFAEwCRrDEYmOM0dgzqujJY5M9v81ZLkvH/xVe1LsDgICti83gvXshgZsnd2DKmcmXV+rlc+n/GwjuHBaRAUtRsSjXKIaZYVpJok4xu+3I1kpIyo9Kx1yeLDR37WckbnfLcEgFK2SOTSVzeRJeuQeEiTLjvtgZxK4Ge9b8nJj9/X/XUDAYISV0UGbt0JZcZPB6X6CJNfNFeGAOu81QZnRngQlECpj2D1nkIKweo0P8uJH4dRGC5o8uACIxQqAIKiynzrjJZeiK0Dwe1HnEBQFHfL5n9j9kqDS/A4CEr1dLEHCtTOQdKqzLEvZ5I0IUqJXZZ5Z/SvMp5JlaNUMYA0y0w4CxvnYwJvoJdJlreefuvEJf0z7CAoGWOnFKInkhnnCjfNxWmBoOECURAlDecIDhCUgEFQmCKoCWRLx+jhLvOJD44yWpsGUjBGt7EJxHzILGbSY8qAZO+7OUqAZMEI3RVgKUmAoBTnA9my+JhGzC/mZpn+650dxdXPWBz0VyEkrKNlET8ISpEAVdm6lwgCNCXlsg27yBqWm3LTak2TJVIgKEpwSJaoRIYhTQXLEY5XnmYoXOuSkG8ET4NafRmKWAgP+ZIpNo+bG0Z8fKhOK0yysMOVE0YnCEq0rDUpDDN0WpkgUY8BU1Pc9mAtvaLOMnFwlZxR8Jv9bZTTrk7AuEBQSq3dg2i/uOGlcCwh3RHJup0ljjMFg6CMT22SXl+5rRfdR1y6gyK4kfH6guxEeoXF1D2SjcX8jPStCD9CKXEbFQZB8UnJjCTiRPk8VxCkb09IxZnhWRMoScXxZQTEiTiL1kVgKC7dFcKM5huomAp64dPz//7MKoqaKJ9tKby4RTkHBt0wfXe0XyWQM0Yrq0SjbYtbtz/32LI/BbVQtk3bJxeGrLaBUdTQuiLqH/ulfDTFFCS34y96tjhLM+VCUTWMQPzIUG9RRXZYngqGR3+ttFmNMrzaskYuuJwYRXv9QjwWiyWSyURMJfF4mLH399lG6HBcKWODNlv/uNisNjwazx8IoAN9JQfkY7fcbKzsjjoSD3o8rEq4gAceKkZ1b1v25z47pi7XQDnw0oZ575t5NkmeomiK4ot+OcNTtEoovhgGJ30MQRWPUhRJ83X73543LDtznx/MWKuBspVD5rbdhQaihzJ13S3rh8uaDlaifLEjNvbI4u6GQTk2Y/HmdS0zftpRidK28uVXl0/d3ji9Mm1zOMrumbMJLkdxrHnl3PkjLS1Uw6DIZk+tmPpaOcrxt/LbI/PfahSUf1rybji6dtqRMpSzKy/mtxebfvR1g6Bst7QlxdCBmavK5i9Tnr7/3fz2nSWLftsYKvb1Lxb85JmtT7SsuVJu9sO9cshL9vc2yH82pazdN7p7hipDh8m/BZxEmUSZRJlEmUSpp/wf1YVyh9xQCNcAAAAASUVORK5CYII=)
Answer:Given:- ABCD is parallelogram
BP=BD/3
DQ=BD/3
Formula used:- SAS congruency property
If 2 sides and angle between the two sides of both
the triangle are equal, then both triangle are congruent
Solution:-
⇒ In parallelogram ABCD
AO=OC and DO=OB [diagonal of parallelogram bisect each other]
As DO=OB
Where DO=DQ+OQ
OB=OP+PB
∴ DQ+OQ=OP+PB
⇒
+OQ=OP+![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAfCAMAAADdjm27AAAAAXNSR0IArs4c6QAAAHVQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7Zm27aQ27ZmkLbbZrb/Zrbb25Bm25A6ZpDbZpC2OpDbtmYAkGY6Oma2OmaQkDo6AGa2kDoAZjoAOjoAADqQADpmADo6ZgA6ZgAAOgA6OgAAAABmAAA6AAAAYFuLCAAAAAF0Uk5TAEDm2GYAAACPSURBVHjaxZHNDoIwEIQH11ZABQX8t4LW7vs/Imm2gtKLF+Ocvkw2s5Nd4Ctpy8x8Wwi4PQHInnOo+0kgt4aE0BgS0HYtlu4CIDnXQOazahqsEKFeEKY8baKsYUpdDIVehwBtRfi1OBL+pfLKbvvhJMcVli6NvveYWmpXTJyG2yLakPurj5p1qTzivYQdS/TgXA7kcRBCAgAAAABJRU5ErkJggg==)
⇒ OQ=OP+
- ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAfCAMAAADdjm27AAAAAXNSR0IArs4c6QAAAHVQTFRFAAAA///b//+22///tv///9u2/9uQttv/kNv//7Zm27aQ27ZmkLbbZrb/Zrbb25Bm25A6ZpDbZpC2OpDbtmYAkGY6Oma2OmaQkDo6AGa2kDoAZjoAOjoAADqQADpmADo6ZgA6ZgAAOgA6OgAAAABmAAA6AAAAYFuLCAAAAAF0Uk5TAEDm2GYAAACPSURBVHjaxZHNDoIwEIQH11ZABQX8t4LW7vs/Imm2gtKLF+Ocvkw2s5Nd4Ctpy8x8Wwi4PQHInnOo+0kgt4aE0BgS0HYtlu4CIDnXQOazahqsEKFeEKY8baKsYUpdDIVehwBtRfi1OBL+pfLKbvvhJMcVli6NvveYWmpXTJyG2yLakPurj5p1qTzivYQdS/TgXA7kcRBCAgAAAABJRU5ErkJggg==)
⇒ OQ=OP
PQ = OP+OQ = 2(OQ) = 2(OP)
∴ AC diagonal bisect PQ
⇒ In Δ QOC and Δ POA
OQ=PO [Proven above]
AO=OC [Diagonal of parallelogram bisect each other]
∠ QOC=∠ AOP [vertically opposite angles]
Hence Δ QOC ≅ Δ POA
∴ ∠ CQO=∠ OPA
If QC and PA are 2 lines
And QP is the transverse
And ∠ CQO=∠ OPA by Alternate angles
∴ QC||PA
Conclusion:-
CQ||PA and CA is bisector of PQ.
Question 9.ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH. Prove that EFGH is a square.
![](data:image/jpeg;base64,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)
Answer:Given:- *ABCD is a square
*E, F, G and H are the mid points of AB, BC, CD and DA
respectively
*AE = BF = CG = DH
Formula used:- *Isosceles Δ property
⇒ If 2 sides of triangle are equal then
Corresponding angle will also be equal
*Properties of quadrilateral to be square
⇒ All sides are equal
⇒ All angles are 90°
Solution:-
In Δ AHE, Δ EBF, Δ FCG, Δ DHG
⇒ AE = BF = CG = DH [Given]
If;
⇒ AE=EB [E is midpoint of AB]
⇒ BF=FC [F is midpoint of BC]
⇒ CG=GD [G is midpoint of CD]
⇒ DH=HA [H is midpoint of DA]
⇒ AE = BF = CG = DH
On replacing every part we get;
⇒ EB=FC=GD=HA;
⇒ ∠ A+∠ B+∠ C+∠ D=90° [All angles of square are 90°]
Hence;
All triangles Δ AHE, Δ EBF, Δ FCG, Δ DHG
are congruent by SAS property
∴ Δ AHE≅ Δ EBF≅ Δ FCG ≅ Δ DHG
⇒ HE=EF=FG=GH [All triangles are congruent]
In Δ AHE, Δ EBF, Δ FCG, Δ DHG
∵ all sides of square are equal and after the midpoint of each sides
Every half side of square are equal to half of other sides.
HA=AE , EB=FB ,FC=GC ,HD=DG
∴ All Δ AHE, Δ EBF, Δ FCG, Δ DHG are isosceles
⇒ as central angle of all triangle is 90°
It makes all Δ AHE, Δ EBF, Δ FCG, Δ DHG are right angle isosceles Δ
∴ all corresponding angles of equal side will be 45°
∠ AHE=∠ BEF=∠ CFG=∠ DHG=∠ AEH=∠ BFE=∠ CGF=∠ DGH=45°
⇒ as AB is straight line
Then; ∠ AEH+∠ HEF+∠ BEF=180°
45°+∠ HEF+45° =180°
∠ HEF=180° -90° =90°
Similarly ;
∠ EFG=90°
∠ FGH=90°
∠ GHE=90°
Conclusion:-
All angles are 90° and all sides are equal of quadrilateral
Hence quadrilateral is square
The opposite angles of a parallelogram are and
Find the measure of each angle of the parallelogram.
Answer:
Given:- Opposite angles of parallelogram and
Formula used:- opposite angles of a parallelogram are equal
Corresponding angles sum is 180°
Solution:-
Let ∠ A and ∠ C
∠ A = ∠ C [opposite angles of a parallelogram are equal]
3x-2=x+48
3x – x=48+2
2x=50
x=25
Then;
∠ A=∠ C=x+48=25+ 48 = 73°
∠ A+∠ B=180°
∠ B=180° - 73°
∠ B= 107°
∠ B = ∠ D [opposite angles of a parallelogram are equal]
Conclusion:-
Angles of parallelogram = 73°, 107°, 73°, 107°
Question 2.
Find the measure of all the angles of a parallelogram, if one angle is 24° less than the twice of the smallest angle.
Answer:
Given:- one angle is 24° less than the twice of the smallest angle
Formula used:- opposite angles of a parallelogram are equal
Corresponding angles sum is 180°
Solution:-
Let ∠ A and ∠ C be smallest because
∠ A = ∠ C [opposite angles of a parallelogram are equal]
2∠ A+ 24° =∠ B
∠ A+∠ B=180° [Sum of corresponding angles is 180° ]
∠ B=180°-∠ A
Then,
2∠ A+ 24° =180° -∠ A
3∠ A =180° - 24°
3∠ A=156°
∠ A==52°
∠ B=180° -∠ A
∠ B= 180° -52°
∠ B=128°
∠ B = ∠ D [opposite angles of a parallelogram are equal]
Conclusion:-
∴ Angles of parallelogram = 52°, 128°, 52°, 128°
Question 3.
In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB.
Answer:
Given :- ABCD is a parallelogram
And CE=EB
Formula used:- ASA congruency property
If 2 angles and one side between them in two
triangles are equal then both triangle are congruent
Solutions :-
In Δ DCE and Δ FBE
∠ DEC=∠ BEF [Vertically opposite angles]
As DC || BF
∠ ECD=∠ EBF [Alternate angles]
And;
CE=EB [Given]
∴ Δ DCE ≅ Δ FBE
As Δ DCE ≅ Δ FBE
Then
DC=BF
And DC=AB [opposite sides of parallelogram are equal]
Hence ;
AB=BF
AF=AB+BF
AF=2AB.
Hence Proved;
Question 4.
In the adjacent figure ABCD is a parallelogram P, Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.
Answer:
Given:-ABCD is a parallelogram
P,Q are the midpoints of sides AB and DC respectively.
Solution:-
In parallelogram ABCD
If P,Q are the midpoints of sides AB and DC respectively
∴ DC=2QC=2QD
∴ AB=2AP=2PB
If DC||AB
Then;
QD||AP and QC||PB
Line PQ divides the parallelogram in 2 equal parts
Because P and Q are midpoints
∴ AD||PQ||CB
If;
PQ||CB and QC||PB
Then, PBCQ is also a parallelogram
Question 5.
ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD || BA as shown in the figure. Show that
(i) ∠DAC = ∠BCA
(ii) ABCD is a parallelogram
Answer:
Given:- AB=AC and ABC is isosceles triangle
∠ QAD=∠ DAC
CD||BA
Formula used:- sum of angles of triangle is 180°
Solution:-
As Δ ABC is a isosceles triangle
∠ ABC=∠ ACB
∠ ABC+∠ ACB+∠ CAB=180°
2∠ ACB+∠ CAB=180°
*As BAQ is a straight line
∠ CAB+∠ DAC+∠ QAD=180°
*∠ QAD=∠ DAC [Given]
∠ CAB=180° - 2∠ DAC
Putting value of ∠ CAB in above equation 1
2∠ ACB+180° - 2∠ DAC=180°
2∠ ACB =2∠ DAC
∠ ACB =∠ DAC
If;
There is ∠ ACB =∠ DAC and AC is the transverse
∴ these are equal by alternate angles
And AD||BC
In ABCD
If;
AD||BC & CD||BA
If both pair of sides of quadrilateral are parallel
Then the quadrilateral is parallelogram
Conclusion:-
ABCD is a parallelogram
And ∠DAC = ∠BCA
Question 6.
ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that
(i) Δ APB ≅ Δ CQD
(ii) AP = CQ
Answer:
Given:- ABCD is parallelogram
Formula used :- AAS property
If 2 angles and any one side is are equal in both triangle
Then both triangles are congruent
Solution:-
In Δ APB and Δ CQD
∠ CQD=∠ APB=90°
If ABCD is a parallelogram
∠ CDB=∠ DBA [alternate angles as DC||AB]
AB=DC [opposite sides of parallelogram are equal]
By AAS property
∴ Δ APB ≅ Δ CQD
If Δ APB ≅ Δ CQD
Then
AP=CQ
Conclusion:-
In parallelogram ABCD; Δ APB ≅ Δ CQD
Question 7.
In and DEF, AB || DE, AB=DE; BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that
(i) ABED is a parallelogram
(ii) BCFE is a parallelogram
(iii) AC = DF
(iv) ∆ABC ≅ ∆DEF
Answer:
Given:- AB||DE , AB=DE; BC||EF, BC=EF
Formula used:- SSS congruency rule
If all 3 sides of both triangle are equal then
Both triangles are congruent.
Solution:-
(1) In ABED
AB||DE
AB=DE
∴ ABED is a parallelogram
∵ If one pair of side in quadrilateral is equal and parallel
Then the quadrilateral is parallelogram.
(2) In BCFE
BC||EF
BC=EF
∴ BCEF is a parallelogram
∵ If one pair of side in quadrilateral is equal and parallel
Then the quadrilateral is parallelogram.
(3) As ABED is a parallelogram
BE||AD , BE=AD ;
As BCFE is a parallelogram
BE||CF , BE=CF ;
∴ By concluding both above statements
AD||CF and AD=CF
∴ ACFD is a parallelogram
∵ If one pair of side in quadrilateral is equal and parallel
Then the quadrilateral is parallelogram
If ACDF is a parallelogram ;
Then
AC=DF [opposite sides of parallelogram are equal ]
(4) In Δ ABC and Δ DEF
AB=DE [Given]
BC=EF [Given]
AC=DF [Proved above]
Δ ABC ≅ Δ DEF [SSS congruency rule]
Question 8.
ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ || AP and also AC bisects PQ (see figure).
Answer:
Given:- ABCD is parallelogram
BP=BD/3
DQ=BD/3
Formula used:- SAS congruency property
If 2 sides and angle between the two sides of both
the triangle are equal, then both triangle are congruent
Solution:-
⇒ In parallelogram ABCD
AO=OC and DO=OB [diagonal of parallelogram bisect each other]
As DO=OB
Where DO=DQ+OQ
OB=OP+PB
∴ DQ+OQ=OP+PB
⇒ +OQ=OP+
⇒ OQ=OP+ -
⇒ OQ=OP
PQ = OP+OQ = 2(OQ) = 2(OP)
∴ AC diagonal bisect PQ
⇒ In Δ QOC and Δ POA
OQ=PO [Proven above]
AO=OC [Diagonal of parallelogram bisect each other]
∠ QOC=∠ AOP [vertically opposite angles]
Hence Δ QOC ≅ Δ POA
∴ ∠ CQO=∠ OPA
If QC and PA are 2 lines
And QP is the transverse
And ∠ CQO=∠ OPA by Alternate angles
∴ QC||PA
Conclusion:-
CQ||PA and CA is bisector of PQ.
Question 9.
ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH. Prove that EFGH is a square.
Answer:
Given:- *ABCD is a square
*E, F, G and H are the mid points of AB, BC, CD and DA
respectively
*AE = BF = CG = DH
Formula used:- *Isosceles Δ property
⇒ If 2 sides of triangle are equal then
Corresponding angle will also be equal
*Properties of quadrilateral to be square
⇒ All sides are equal
⇒ All angles are 90°
Solution:-
In Δ AHE, Δ EBF, Δ FCG, Δ DHG
⇒ AE = BF = CG = DH [Given]
If;
⇒ AE=EB [E is midpoint of AB]
⇒ BF=FC [F is midpoint of BC]
⇒ CG=GD [G is midpoint of CD]
⇒ DH=HA [H is midpoint of DA]
⇒ AE = BF = CG = DH
On replacing every part we get;
⇒ EB=FC=GD=HA;
⇒ ∠ A+∠ B+∠ C+∠ D=90° [All angles of square are 90°]
Hence;
All triangles Δ AHE, Δ EBF, Δ FCG, Δ DHG
are congruent by SAS property
∴ Δ AHE≅ Δ EBF≅ Δ FCG ≅ Δ DHG
⇒ HE=EF=FG=GH [All triangles are congruent]
In Δ AHE, Δ EBF, Δ FCG, Δ DHG
∵ all sides of square are equal and after the midpoint of each sides
Every half side of square are equal to half of other sides.
HA=AE , EB=FB ,FC=GC ,HD=DG
∴ All Δ AHE, Δ EBF, Δ FCG, Δ DHG are isosceles
⇒ as central angle of all triangle is 90°
It makes all Δ AHE, Δ EBF, Δ FCG, Δ DHG are right angle isosceles Δ
∴ all corresponding angles of equal side will be 45°
∠ AHE=∠ BEF=∠ CFG=∠ DHG=∠ AEH=∠ BFE=∠ CGF=∠ DGH=45°
⇒ as AB is straight line
Then; ∠ AEH+∠ HEF+∠ BEF=180°
45°+∠ HEF+45° =180°
∠ HEF=180° -90° =90°
Similarly ;
∠ EFG=90°
∠ FGH=90°
∠ GHE=90°
Conclusion:-
All angles are 90° and all sides are equal of quadrilateral
Hence quadrilateral is square
Exercise 8.4
Question 1.ABC is a triangle. D is a point on AB such that
and E is a point on AC such that
If DE = 2 cm find BC.
Answer:![](data:image/jpeg;base64,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)
Given:- DE=2cm
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Formula used:- Line joining midpoints of 2 sides of triangle will be
half of its 3rd side.
Solution:-
Assume mid points of line AB and AC is M and N
The formation of new triangle will be there Δ AMN
As;
⇒ AC=4AE
and ![](data:image/png;base64,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)
∴ AM=2AE
Hence;
E is the midpoint of AM
Similarly
D is the midpoint of AN
→ In Δ AMN
If E,D are midpoints
ED=
MN
MN=2ED
MN=2×2cm=4cm
→ In Δ ABC
If M,N are midpoints
AB=
MN
AB=2MN
AB=2×4cm=8cm
Conclusion:-
BC=8cm
Question 2.ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.
Answer:![](data:image/jpeg;base64,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)
Given:- ABCD is quadrilateral E, F, G and H are the midpoints of
AB, BC, CD and DA respectively
Formula used:- Line joining midpoints of 2 sides of triangle
Is parallel to 3rd side
Solution:-
BD is diagonal of quadrilateral
EH is the line joined by midpoints of triangle ABD,
∴EH is parallel to BD
GF is line joined by midpoints of side BC&BD of triangle BCD
∴GF is parallel to BD
⇒ If HE is parallel to BD and BD is parallel to GF
∴ It gives HE is parallel to GF
⇒ AC is another diagonal of quadrilateral
GH is the line joined by midpoints of triangle ADC,
∴GH is parallel to AC
FE is line joined by midpoints of side BC&AB of triangle ABC
∴FE is parallel to AC
⇒ If GH is parallel to AC and AC is parallel to FE
∴ It gives GH is parallel to FE
As HE||GF and GH||FE
∴ EFGH is a parallelogram
Conclusion:-
EFGH is a parallelogram
Question 3.Show that the figure formed by joining the midpoints of sides of a rhombus successively is a rectangle.
Answer:![](data:image/jpeg;base64,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)
Given:- ABCD is a rhombus
E,F,G,H are the mid points of AB,BC,CD,DA
Formula used:- Line joining midpoints of 2 sides of triangle
Is parallel and half of 3rd side
Solution:-
BD is diagonal of rhombus
EH is the line joined by midpoints of triangle ABD,
∴EH is parallel and half of BD
GF is line joined by midpoints of side BC&BD of triangle BCD
∴GF is parallel and half BD
⇒ If HE is parallel to BD and BD is parallel to GF
∴ It gives HE is parallel to GF
⇒ If HE is half of BD and GF is also half of BD
∴ It gives HE is equal to GF
⇒ AC is another diagonal of rhombus
GH is the line joined by midpoints of triangle ADC,
∴GH is parallel to AC
∴GH is half of AC
FE is line joined by midpoints of side BC&AB of triangle ABC
∴FE is parallel to AC
∴ FE is half of AC
⇒ If GH is parallel to AC and AC is parallel to FE
∴ It gives GH is parallel to FE
⇒ If GH is half of AC and FE is also half of AC
∴ It gives GH is equal to FE
As diagonals of rhombus intersect at 90°
And AC is parallel to FE and GH
All angles of EFGH is 90°
All angles are 90° and opposite sides are equal and parallel
Conclusion:-
EFGH is a rectangle
Question 4.In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC respectively. Show that the line segments AF and EC trisect the diagonal BD.
![](data:image/png;base64,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)
Answer:Given:- ABCD is a parallelogram
E and F are the midpoints of the sides AB and DC respectively
Formula used:- Line drawn through midpoint of one side of triangle
Parallel to other side , bisect the 3rd side.
Solution:-
As ABCD is parallelogram
AB=CD and AB||CD;
⇒ AE=CF and AE||CF [E and F are the midpoints of AB and CD]
In quadrilateral AECF
⇒ AE=CF and AE||CF
AECF is a parallelogram.
∵ Quadrilateral having one pair of side equal and parallel are parallelogram
If AECF is a parallelogram
∴ AF||CE
Hence ;
PF||CQ and AP||QE [As AF=AP+PF and CE=CQ+QE ]
In Δ DQC
DF=FC [F is midpoint]
PF||CQ
Then;
P is midpoint of DQ
DP=PQ
∵ Line drawn through midpoint of one side of triangle Parallel to
other side , bisect the 3rd side
In Δ APB
AE=EB [E is midpoint]
AP||QE
Then;
Q is midpoint of PB
PQ=QB
∵ Line drawn through midpoint of one side of triangle Parallel to
other side , bisect the 3rd side
If DP=PQ and PQ=QB
Then DP=PQ=QB
Conclusion:-
Line segments AF and EC trisect the diagonal BD.
Question 5.Show that the line segments joining the midpoints of the opposite sides of a quadrilateral and bisect each other.
Answer:![](data:image/jpeg;base64,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)
Given:- ABCD is a quadrilateral
Formula used:- Line joining midpoints of 2 sides of triangle
Is parallel and half of 3rd side
Solution:-
BD is diagonal of quadrilateral
EH is the line joined by midpoints of triangle ABD,
∴EH is parallel and half of BD
GF is line joined by midpoints of side BC&BD of triangle BCD
∴GF is parallel and half BD
⇒ If HE is parallel to BD and BD is parallel to GF
∴ It gives HE is parallel to GF
⇒ If HE is half of BD and GF is also half of BD
∴ It gives HE is equal to GF
⇒ AC is another diagonal of quadrilateral
GH is the line joined by midpoints of triangle ADC,
∴GH is parallel to AC
∴GH is half of AC
FE is line joined by midpoints of side BC&AB of triangle ABC
∴FE is parallel to AC
∴ FE is half of AC
⇒ If GH is parallel to AC and AC is parallel to FE
∴ It gives GH is parallel to FE
⇒ If GH is half of AC and FE is also half of AC
∴ It gives GH is equal to FE
If both opposite sides are parallel and equal
Then, the quadrilateral is parallelogram
If EFGH is parallelogram
Then their diagonal bisect each other
If diagonal of parallelogram is the line joining midpoint of opposite sides of quadrilateral
Then;
Line joining midpoints of opposite sides of quadrilateral bisect each other.
Conclusion:-
Lines joining midpoints of opposite sides of quadrilateral bisect each other
Question 6.ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and Parallel to BC intersects AC at D. Show that
(i) D is the midpoint of AC
(ii) MD ⊥ AC
(iii) CM = MA =
AB
![](data:image/png;base64,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)
Answer:Given:- ACB is right angle triangle
M is midpoint of AB
DM||CB
Formula used:- Line drawn through midpoint of one side of triangle
Parallel to other side , bisect the 3rd side
* SAS congruency property
If 2 sides and angle between the two sides of both
the triangle are equal, then both triangle are congruent
Solution:-
(1) In Δ ABC
M is midpoint of AB
And DM||CB
∴ D is midpoint of AC
AD=DC
∵ Line drawn through midpoint of one side of triangle
Parallel to other side , bisect the 3rd side
(2) In Δ ABC
DM||CB
∠ ADM=∠ ACB [Corresponding angles]
∠ ACB =90°
∠ ADM=90°
(3) In Δ ADM and Δ DMC
⇒ DM=DM [Common in both triangles ]
⇒ AD=DC [D is the midpoint]
As ADC is straight line
∠ ADM+∠ MDC=180°
∠ MDC=180° - ∠ ADM
∠ MDC=90°
⇒ ∠ ADM=∠ MDC
Hence;
In Δ ADM ≅ Δ DMC
∴ CM=MA
⇒ MA=
AB [M is midpoint of AB]
∴ CM=MA=
AB
ABC is a triangle. D is a point on AB such that and E is a point on AC such that
If DE = 2 cm find BC.
Answer:
Given:- DE=2cm
Formula used:- Line joining midpoints of 2 sides of triangle will be
half of its 3rd side.
Solution:-
Assume mid points of line AB and AC is M and N
The formation of new triangle will be there Δ AMN
As;
⇒ AC=4AE
and
∴ AM=2AE
Hence;
E is the midpoint of AM
Similarly
D is the midpoint of AN
→ In Δ AMN
If E,D are midpoints
ED=MN
MN=2ED
MN=2×2cm=4cm
→ In Δ ABC
If M,N are midpoints
AB=MN
AB=2MN
AB=2×4cm=8cm
Conclusion:-
BC=8cm
Question 2.
ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.
Answer:
Given:- ABCD is quadrilateral E, F, G and H are the midpoints of
AB, BC, CD and DA respectively
Formula used:- Line joining midpoints of 2 sides of triangle
Is parallel to 3rd side
Solution:-
BD is diagonal of quadrilateral
EH is the line joined by midpoints of triangle ABD,
∴EH is parallel to BD
GF is line joined by midpoints of side BC&BD of triangle BCD
∴GF is parallel to BD
⇒ If HE is parallel to BD and BD is parallel to GF
∴ It gives HE is parallel to GF
⇒ AC is another diagonal of quadrilateral
GH is the line joined by midpoints of triangle ADC,
∴GH is parallel to AC
FE is line joined by midpoints of side BC&AB of triangle ABC
∴FE is parallel to AC
⇒ If GH is parallel to AC and AC is parallel to FE
∴ It gives GH is parallel to FE
As HE||GF and GH||FE
∴ EFGH is a parallelogram
Conclusion:-
EFGH is a parallelogram
Question 3.
Show that the figure formed by joining the midpoints of sides of a rhombus successively is a rectangle.
Answer:
Given:- ABCD is a rhombus
E,F,G,H are the mid points of AB,BC,CD,DA
Formula used:- Line joining midpoints of 2 sides of triangle
Is parallel and half of 3rd side
Solution:-
BD is diagonal of rhombus
EH is the line joined by midpoints of triangle ABD,
∴EH is parallel and half of BD
GF is line joined by midpoints of side BC&BD of triangle BCD
∴GF is parallel and half BD
⇒ If HE is parallel to BD and BD is parallel to GF
∴ It gives HE is parallel to GF
⇒ If HE is half of BD and GF is also half of BD
∴ It gives HE is equal to GF
⇒ AC is another diagonal of rhombus
GH is the line joined by midpoints of triangle ADC,
∴GH is parallel to AC
∴GH is half of AC
FE is line joined by midpoints of side BC&AB of triangle ABC
∴FE is parallel to AC
∴ FE is half of AC
⇒ If GH is parallel to AC and AC is parallel to FE
∴ It gives GH is parallel to FE
⇒ If GH is half of AC and FE is also half of AC
∴ It gives GH is equal to FE
As diagonals of rhombus intersect at 90°
And AC is parallel to FE and GH
All angles of EFGH is 90°
All angles are 90° and opposite sides are equal and parallel
Conclusion:-
EFGH is a rectangle
Question 4.
In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC respectively. Show that the line segments AF and EC trisect the diagonal BD.
Answer:
Given:- ABCD is a parallelogram
E and F are the midpoints of the sides AB and DC respectively
Formula used:- Line drawn through midpoint of one side of triangle
Parallel to other side , bisect the 3rd side.
Solution:-
As ABCD is parallelogram
AB=CD and AB||CD;
⇒ AE=CF and AE||CF [E and F are the midpoints of AB and CD]
In quadrilateral AECF
⇒ AE=CF and AE||CF
AECF is a parallelogram.
∵ Quadrilateral having one pair of side equal and parallel are parallelogram
If AECF is a parallelogram
∴ AF||CE
Hence ;
PF||CQ and AP||QE [As AF=AP+PF and CE=CQ+QE ]
In Δ DQC
DF=FC [F is midpoint]
PF||CQ
Then;
P is midpoint of DQ
DP=PQ
∵ Line drawn through midpoint of one side of triangle Parallel to
other side , bisect the 3rd side
In Δ APB
AE=EB [E is midpoint]
AP||QE
Then;
Q is midpoint of PB
PQ=QB
∵ Line drawn through midpoint of one side of triangle Parallel to
other side , bisect the 3rd side
If DP=PQ and PQ=QB
Then DP=PQ=QB
Conclusion:-
Line segments AF and EC trisect the diagonal BD.
Question 5.
Show that the line segments joining the midpoints of the opposite sides of a quadrilateral and bisect each other.
Answer:
Given:- ABCD is a quadrilateral
Formula used:- Line joining midpoints of 2 sides of triangle
Is parallel and half of 3rd side
Solution:-
BD is diagonal of quadrilateral
EH is the line joined by midpoints of triangle ABD,
∴EH is parallel and half of BD
GF is line joined by midpoints of side BC&BD of triangle BCD
∴GF is parallel and half BD
⇒ If HE is parallel to BD and BD is parallel to GF
∴ It gives HE is parallel to GF
⇒ If HE is half of BD and GF is also half of BD
∴ It gives HE is equal to GF
⇒ AC is another diagonal of quadrilateral
GH is the line joined by midpoints of triangle ADC,
∴GH is parallel to AC
∴GH is half of AC
FE is line joined by midpoints of side BC&AB of triangle ABC
∴FE is parallel to AC
∴ FE is half of AC
⇒ If GH is parallel to AC and AC is parallel to FE
∴ It gives GH is parallel to FE
⇒ If GH is half of AC and FE is also half of AC
∴ It gives GH is equal to FE
If both opposite sides are parallel and equal
Then, the quadrilateral is parallelogram
If EFGH is parallelogram
Then their diagonal bisect each other
If diagonal of parallelogram is the line joining midpoint of opposite sides of quadrilateral
Then;
Line joining midpoints of opposite sides of quadrilateral bisect each other.
Conclusion:-
Lines joining midpoints of opposite sides of quadrilateral bisect each other
Question 6.
ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and Parallel to BC intersects AC at D. Show that
(i) D is the midpoint of AC
(ii) MD ⊥ AC
(iii) CM = MA = AB
Answer:
Given:- ACB is right angle triangle
M is midpoint of AB
DM||CB
Formula used:- Line drawn through midpoint of one side of triangle
Parallel to other side , bisect the 3rd side
* SAS congruency property
If 2 sides and angle between the two sides of both
the triangle are equal, then both triangle are congruent
Solution:-
(1) In Δ ABC
M is midpoint of AB
And DM||CB
∴ D is midpoint of AC
AD=DC
∵ Line drawn through midpoint of one side of triangle
Parallel to other side , bisect the 3rd side
(2) In Δ ABC
DM||CB
∠ ADM=∠ ACB [Corresponding angles]
∠ ACB =90°
∠ ADM=90°
(3) In Δ ADM and Δ DMC
⇒ DM=DM [Common in both triangles ]
⇒ AD=DC [D is the midpoint]
As ADC is straight line
∠ ADM+∠ MDC=180°
∠ MDC=180° - ∠ ADM
∠ MDC=90°
⇒ ∠ ADM=∠ MDC
Hence;
In Δ ADM ≅ Δ DMC
∴ CM=MA
⇒ MA=AB [M is midpoint of AB]
∴ CM=MA=AB