Class 9th Mathematics AP Board Solution
Exercise 3.1- Answer the following: i. How many dimensions a solid has? ii. How many books are…
- State whether the following statements are true or false? Also give reasons for…
- In the figure given below, show that length AH AB + BC + CD.
- If a point Q lies between two points P and R such that PQ = QR, prove that PQ =…
- Draw an equilateral triangle whose sides are 5.2 cm each.
- What is a conjecture? Give an example for it.
- Mark two points P and Q. Draw a line through P and Q. Now how many lines are…
- In the adjacent figure, a line n falls on lines l and m such that the sum of the…
- In the adjacent figure, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation…
- In the adjacent figure, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that…
- Answer the following: i. How many dimensions a solid has? ii. How many books are…
- State whether the following statements are true or false? Also give reasons for…
- In the figure given below, show that length AH AB + BC + CD.
- If a point Q lies between two points P and R such that PQ = QR, prove that PQ =…
- Draw an equilateral triangle whose sides are 5.2 cm each.
- What is a conjecture? Give an example for it.
- Mark two points P and Q. Draw a line through P and Q. Now how many lines are…
- In the adjacent figure, a line n falls on lines l and m such that the sum of the…
- In the adjacent figure, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation…
- In the adjacent figure, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that…
Exercise 3.1
Question 1.Answer the following:
i. How many dimensions a solid has?
ii. How many books are there in Euclid’s Elements?
iii. Write the number of faces of a cube and cuboid.
iv. What is sum of interior angles of a triangle?
v. Write three un-defined terms of geometry.
Answer:i. A solid has 3 dimensions, namely length, breadth and height.
ii. Euclid of Alexandria in Egypt wrote 13 books called ‘The Elements’.
iii. A cube is also a cuboid having 6 faces. Hence, both cube and cuboid have 6 faces.
iv. By equivalent of fifth postulate, we know that the sum of angle of a triangle is a constant and is equal to two right angles.
∴ Sum of interior angles of a triangle = 180°
v. In geometry, a point, a line and a plane are the un-defined terms.
Question 2.State whether the following statements are true or false? Also give reasons for your answers.
a) Only one line can pass through a given point.
b) All right angles are equal.
c) Circles with same radii are equal.
d) A finite line can be extended on its both sides endlessly to get a straight line.
![](data:image/png;base64,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)
e) From the figure, AB > AC
Answer:a) False
It is false because through a given point, infinite number of lines can pass.
b) True
![](data:image/png;base64,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)
Let us consider ∠ABC = 90°, ∠DEF = 90° and ∠GHI = 90°.
Here, ∠ABC = ∠DEF = ∠GHI
i.e. all the right angles are equal (By Postulate 4).
c) True
Two circles coincide if we superimpose the region bounded by one circle on the other circle. Then, their centers and boundaries also coincide.
∴ Circle with same radii will be equal.
d) True
It is true by Euclid’s postulate 2.
e) True
C is the midpoint of line segment AB dividing the lines into two halves i.e. AC = BC
⇒ AB = AC + BC
∴ AB > AC
Question 3.In the figure given below, show that length AH > AB + BC + CD.
![](data:image/png;base64,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)
Answer:Given figure is drawn above.
By Euclid’s Axiom 5,
We know that ‘The whole is greater than the part’.
In the figure, AH is whole.
AB, BC, CD are parts.
⇒ AB + BC + CD is also a part.
∴ AH > AB + BC + CD
Question 4.If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.
Answer:Given, a point Q lies between 2 points P and R such that PQ = QR.
![](data:image/png;base64,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)
Adding PQ on both sides,
⇒ PQ + PQ = QR + PQ
⇒ 2PQ = PR
∴ PQ = 1/2 PR
Hence proved.
Question 5.Draw an equilateral triangle whose sides are 5.2 cm each.
Answer:Step 1:
Draw a line segment AB of length 5.2 cm.
![](data:image/png;base64,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)
Step2:
From Euclid’s third postulate, we know that we can draw a circle with any center and any radius.
Draw a circle with center A and radius AB.
![](data:image/png;base64,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)
Step 3:
Draw another circle with center B and radius BA.
![](data:image/png;base64,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)
Step 4:
The two circles meet at C. Join C to A and B to form ΔABC.
![](data:image/png;base64,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)
Thus, the required equilateral triangle is constructed.
Question 6.What is a conjecture? Give an example for it.
Answer:Sometimes a certain statement that we think is to be true but that is an educated guess based on observations. Such statements which are neither proved nor disproved are called conjectures (hypothesis). Mathematical discoveries often start out as conjectures.
Example: “Every even number greater than 4 can be written as sum of two primes” is a conjecture stated by Gold Bach.
Question 7.Mark two points P and Q. Draw a line through P and Q. Now how many lines are parallel to PQ, can you draw?
Answer:Let us mark 2 points P and Q. Then, draw a line through P and Q.
![](data:image/png;base64,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)
There can be infinite number of parallel lines to PQ. So, we cannot draw all of them.
Question 8.In the adjacent figure, a line n falls on lines l and m such that the sum of the interior angles 1 and 2 is less than 180°, then what can you say about lines l and m.
![](data:image/png;base64,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)
Answer:By Euclid’s Postulate 5,
We know that if a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Given, a line n falls on lines l and m such that the sum of the interior angles 1 and 2 < 180° on the right side of line n.
So, the lines l and m will eventually intersect on the right side of line n.
Question 9.In the adjacent figure, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between∠1 and ∠2 using a Euclid’s postulate.
![](data:image/png;base64,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)
Answer:Given,
∠1 = ∠3, ∠3 = ∠4 … (i)
And ∠2 = ∠4 … (ii)
By Euclid’s axiom 1,
We know that things which are equal to the same things are equal to one another.
∴ From equation (i), ∠1 = ∠4 … (iii)
Then, from equations (ii) and (iii) and by axiom 1,
⇒ ∠1 = ∠2
Question 10.In the adjacent figure, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that BX = BY
![](data:image/png;base64,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)
Answer:Given, AB = BC … (i)
And BX = 1/2 AB and BY = 1/2 BC … (ii)
By Euclid’s axiom 7,
We know that things which are halves of the same thing are equal to one another.
From (i) and (ii),
∴ BX = BY
Answer the following:
i. How many dimensions a solid has?
ii. How many books are there in Euclid’s Elements?
iii. Write the number of faces of a cube and cuboid.
iv. What is sum of interior angles of a triangle?
v. Write three un-defined terms of geometry.
Answer:
i. A solid has 3 dimensions, namely length, breadth and height.
ii. Euclid of Alexandria in Egypt wrote 13 books called ‘The Elements’.
iii. A cube is also a cuboid having 6 faces. Hence, both cube and cuboid have 6 faces.
iv. By equivalent of fifth postulate, we know that the sum of angle of a triangle is a constant and is equal to two right angles.
∴ Sum of interior angles of a triangle = 180°
v. In geometry, a point, a line and a plane are the un-defined terms.
Question 2.
State whether the following statements are true or false? Also give reasons for your answers.
a) Only one line can pass through a given point.
b) All right angles are equal.
c) Circles with same radii are equal.
d) A finite line can be extended on its both sides endlessly to get a straight line.
e) From the figure, AB > AC
Answer:
a) False
It is false because through a given point, infinite number of lines can pass.
b) True
Let us consider ∠ABC = 90°, ∠DEF = 90° and ∠GHI = 90°.
Here, ∠ABC = ∠DEF = ∠GHI
i.e. all the right angles are equal (By Postulate 4).
c) True
Two circles coincide if we superimpose the region bounded by one circle on the other circle. Then, their centers and boundaries also coincide.
∴ Circle with same radii will be equal.
d) True
It is true by Euclid’s postulate 2.
e) True
C is the midpoint of line segment AB dividing the lines into two halves i.e. AC = BC
⇒ AB = AC + BC
∴ AB > AC
Question 3.
In the figure given below, show that length AH > AB + BC + CD.
Answer:
Given figure is drawn above.
By Euclid’s Axiom 5,
We know that ‘The whole is greater than the part’.
In the figure, AH is whole.
AB, BC, CD are parts.
⇒ AB + BC + CD is also a part.
∴ AH > AB + BC + CD
Question 4.
If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.
Answer:
Given, a point Q lies between 2 points P and R such that PQ = QR.
Adding PQ on both sides,
⇒ PQ + PQ = QR + PQ
⇒ 2PQ = PR
∴ PQ = 1/2 PR
Hence proved.
Question 5.
Draw an equilateral triangle whose sides are 5.2 cm each.
Answer:
Step 1:
Draw a line segment AB of length 5.2 cm.
Step2:
From Euclid’s third postulate, we know that we can draw a circle with any center and any radius.
Draw a circle with center A and radius AB.
Step 3:
Draw another circle with center B and radius BA.
Step 4:
The two circles meet at C. Join C to A and B to form ΔABC.
Thus, the required equilateral triangle is constructed.
Question 6.
What is a conjecture? Give an example for it.
Answer:
Sometimes a certain statement that we think is to be true but that is an educated guess based on observations. Such statements which are neither proved nor disproved are called conjectures (hypothesis). Mathematical discoveries often start out as conjectures.
Example: “Every even number greater than 4 can be written as sum of two primes” is a conjecture stated by Gold Bach.
Question 7.
Mark two points P and Q. Draw a line through P and Q. Now how many lines are parallel to PQ, can you draw?
Answer:
Let us mark 2 points P and Q. Then, draw a line through P and Q.
There can be infinite number of parallel lines to PQ. So, we cannot draw all of them.
Question 8.
In the adjacent figure, a line n falls on lines l and m such that the sum of the interior angles 1 and 2 is less than 180°, then what can you say about lines l and m.
Answer:
By Euclid’s Postulate 5,
We know that if a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Given, a line n falls on lines l and m such that the sum of the interior angles 1 and 2 < 180° on the right side of line n.
So, the lines l and m will eventually intersect on the right side of line n.
Question 9.
In the adjacent figure, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between∠1 and ∠2 using a Euclid’s postulate.
Answer:
Given,
∠1 = ∠3, ∠3 = ∠4 … (i)
And ∠2 = ∠4 … (ii)
By Euclid’s axiom 1,
We know that things which are equal to the same things are equal to one another.
∴ From equation (i), ∠1 = ∠4 … (iii)
Then, from equations (ii) and (iii) and by axiom 1,
⇒ ∠1 = ∠2
Question 10.
In the adjacent figure, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that BX = BY
Answer:
Given, AB = BC … (i)
And BX = 1/2 AB and BY = 1/2 BC … (ii)
By Euclid’s axiom 7,
We know that things which are halves of the same thing are equal to one another.
From (i) and (ii),
∴ BX = BY