Exploring Geometrical Figures Class 8th Mathematics AP Board Solution

Class 8th Mathematics AP Board Solution

Exercise 8.1
Question 1.

Name five pairs of congruent objects, you use daily.


Answer:

Congruent Objects have the same size, same shape and same angle. If you place a congruent object in front of a mirror, the image that you see is congruent or "equal" to the object. They completely overlap each other.

Any five pairs of congruent objects you use daily are:


a) Biscuits of same pack


b) All A4 sheets


c) Two bangles


d) Two balls of same brand and same size


e) Two earrings of the same set



Question 2.

Draw two congruent figures. Are they similar? Explain.


Answer:

We know that two figures are “congruent” if they have the same size, same shape and same angle.

When two figures are “similar”, their angles are same. But that does not mean they have to be congruent. Whereas “Congruent” figures are “always similar”.


Example 1:



Above two figures are congruent as they have same size, same shape and same angle and all congruent figures are similar.


Example 2:



Figures given above are similar as they have same angles but are not congruent.



Question 3.

Take two similar shapes. If you slide rotate or flip one of them, does the similarity remain?


Answer:


Two figures shown above are similar to each other as they have same angles.


On rotating figure on left by 180, we get:



We see that the rotated figure is similar to figure on the right.



Question 4.

If Δ ABC ≅ Δ NMO, name the congruent sides and angles.


Answer:

Given: Δ ABC ≅ Δ NMO


Congruent sides:


a) AB = NM


b) BC = MO


c) AC = NO


Congruent angles:


a) ∠A = ∠N


b) ∠B = ∠M


c) ∠C = ∠O



Question 5.

State whether the following statements are true. Explain with reason.

Two squares of side 3 cm each and one of them rotated through 45o are congruent.


Answer:

True


On rotating the square by 45, the length of side, angle and shape remains the same. Hence, they are congruent.



Question 6.

State whether the following statements are true. Explain with reason.

Any two right triangles with hypotenuse 5cm, are congruent.


Answer:

True

For a right angled triangle to have hypotenuse equal to 5 cm, the other two sides have to be 3 cm and 4 cm as the only possible way. As,  by Pythagoras theorem for Right angled triangles. Thus, any two right triangles with hypotenuse 5cm have same angles and are congruent.



Question 7.

State whether the following statements are true. Explain with reason.

Any two circles of radii 4 cm each are congruent.


Answer:

True

Any two circles of radii 4 cm would completely overlap each other when put front of mirror due to same radii of 4 cm. Hence they are congruent.



Question 8.

State whether the following statements are true. Explain with reason.

Two equilateral triangles of side 4 cm each but labeled as ΔABC and ΔLHN are not congruent.


Answer:

False

Two equilateral triangles of side 4 cm and angle 60 each but labeled as ΔABC and ΔLHN would still be congruent as they have same sides and same angles.



Question 9.

State whether the following statements are true. Explain with reason.

Mirror image of a polygon is congruent to the original.


Answer:

True

Mirror image of a polygon would have same sides and angles as the original and thus, is congruent to the original.



Question 10.

Draw a polygon on a square dot sheet. Also draw congruent figures in different directions and mirror image of it.


Answer:



Question 11.

Using a square dot sheet or a graph sheet draw a rectangle and construct a similar figure.

Find the perimeter and areas of both and compare their ratios with the ratio of their corresponding sides.


Answer:


Perimeter = 2(l + b)


= 2(2 + 1)


= 2(3)


= 6 cm


Area = l×b


= 2×1



A figure similar to above figure is shown below:



Perimeter = 




= 12 cm


Area = 




Ratio of the sides of the two figures (fig 2:fig 1) = 2:1


Ratio of the areas of the two figures (fig 2:fig 1) = 3:1


Ratio of the perimeter of the two figures (fig 2:fig 1) = 2:1



Question 12.

7 pillars are used to hold a slant iron ladder as shown in the figure. If the distance between every two pillars is 1 m and height of the last piller is 10.5 m. Find the height of pillar.



Answer:

Given, Distance between every two pillars = 1 m


Height of the last pillar = 10.5 m


Number of pillars used to hold a slant iron ladder = 7


Distance between the tip of ladder on floor to the last pillar = 7 × 1 = 7 cm


Height of last pillar = 10.5 cm


Formula Used:


Pythagoras Theorem: 



 Length of slant ladder = 




= 12.619 cm (ans)


Question 13.

Standing at 5 m apart from a vertical pole of height 3 m, Sudha observed a building at the back of the pillar that tip of the pillar is in line with the top of the building. If the distance between pillar and building is 10 m, estimate the height of the building. [Here height of Sudha is neglected]


Answer:

Let the height of the building be x cm.


In ABC,



In ADE,






Height of building = 9 cm.



Question 14.

Draw a quadrilateral of any measurements. Construct a dilation of scale factor 3. Measure their corresponding sides and verify whether they are similar.


Answer:

Given, Dilation of scale factor = 3

Let’s draw a square with each side = 3 cm



Now on dilating the square using scale factor = 3, then


Each side of the square becomes =  cm



We know that two figures are similar if their angles are same.


In the two squares drawn above we know that each angle = 90


Hence, both the figures are similar.




Exercise 8.2
Question 1.

Cut the bold type English alphabets (capital) and paste in your note book. Draw possible number of lines of symmetry for each of the letter.

(i) How many letters have no linear symmetry?

(ii) How many letters have one line of symmetry?

(iii) How many letters have two lines of symmetry?

(iv) How many letters have more than two lines of symmetry?

(v) Which of them have rotational symmetry?

(vi) Which of them have point symmetry?


Answer:

(i) 9; F,G,J,L,N,P,Q,R,S

(ii) 13; A,B,C,D,E,K,M,T,U,V,W,Y,Z


(iii)3; H,I,X


(iv) 1;O


(v) 1;O


When a shape it looks the same after some rotation by a partial turn, then its said to have rotational symmetry


(vi) 5; H,J,N,O,X


A figure has point symmetry when it looks the same when up-side-down, or when rotated by 180.



Question 2.

Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?



Answer:


Line of symmetry = 2



Line of symmetry = 3



Line of symmetry = 8



Line of symmetry = 10



Line of symmetry = 12



Line of symmetry = 14



Line of symmetry = 16


All of the above figures have point symmetry.



Question 3.

Name some natural objects with faces which have atleast one line of symmetry.


Answer:

Some natural objects with faces which have atleast one line of symmetry are:

a) Moon


b) Sun


c) Human body


d) Star Fish


e) Plant Leaf



Question 4.

Draw three tessellations and name the basic shapes used on your tessellation.


Answer:

A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps.

Basic figure used-Rectangle



Basic figure used-Triangle



Basic figure used-Square



PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

HINDI ENTIRE PAPER SOLUTION

MARATHI PAPER SOLUTION

SSC MATHS I PAPER SOLUTION

SSC MATHS II PAPER SOLUTION

SSC SCIENCE I PAPER SOLUTION

SSC SCIENCE II PAPER SOLUTION

SSC ENGLISH PAPER SOLUTION

SSC & HSC ENGLISH WRITING SKILL

HSC ACCOUNTS NOTES

HSC OCM NOTES

HSC ECONOMICS NOTES

HSC SECRETARIAL PRACTICE NOTES

2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

OCM PAPER SOLUTION 2019 27th, February, 2019

HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

HSC Maharashtra Board Papers 2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

HSC MARATHI MARCH 2020

HSC MATHS MARCH 2020

SSC Maharashtra Board Papers 2020

(Std 10th English Medium)

English MARCH 2020

HindI MARCH 2020

Hindi (Composite) MARCH 2020

Marathi MARCH 2020

Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Sanskrit (Composite) MARCH 2020

Science (Paper 1) MARCH 2020

Science (Paper 2)

MUST REMEMBER THINGS on the day of Exam

Are you prepared? for English Grammar in Board Exam.

Paper Presentation In Board Exam

How to Score Good Marks in SSC Board Exams

Tips To Score More Than 90% Marks In 12th Board Exam

How to write English exams?

How to prepare for board exam when less time is left

How to memorise what you learn for board exam

No. 1 Simple Hack, you can try out, in preparing for Board Exam

How to Study for CBSE Class 10 Board Exams Subject Wise Tips?

JEE Main 2020 Registration Process – Exam Pattern & Important Dates

NEET UG 2020 Registration Process Exam Pattern & Important Dates

How can One Prepare for two Competitive Exams at the same time?

8 Proven Tips to Handle Anxiety before Exams!