SChand Composite Mathematics Class 7 Chapter 13 Congruence of Triangle Exercise 13A

 Exercise 13 A

Question 1 

State whether or not the following pairs of triangles are congruent. If they are, give reasons.

(i) (Image to be added)

Sol: $5 \frac{3}{8} \mathrm{~cm}$ = $\frac{43}{8}$ = 5.375 cm 

1 cm = 10mm

$5.375 \times 10$ = 53.75mm

 $4 \frac{5}{8} \mathrm{~cm}$ = 46.25mm

$6 \frac{1}{8} \mathrm{~cm}$ = 61.25mm

(BY SSS Triangle are congruent each other)

(ii) (Image to be added)

Sol: 62mm converted into Cm = 6.2cm

Triangle are not congruent

(iii)   (Image to be added)

Sol: 40 mm = 4cm 

70 mm = 7cm 

Acc SAS triangle are congruent 

(iv)   (Image to be added)

Sol: not congruent 

(v) (Image to be added)

Sol: (Acc ASA Triangle are equal)

(v) (Image to be added)

Sol: By RHS Triangle are Congruent 

Question 2

Show by comparing angles and sides, which of the triangles given here are congruent to each other .

(Image to be added)

Question 3

In the following figure, state the condition you would use to show that $\triangle A B C$ and $\triangle C D E$ are congruent . 

(IMAGE TO BE ADDED)

Sol: A C=C E

B C=C D

$\angle A C B=\angle DCE$  (Vertically opposite angle)

 By SAS  $\triangle A B C \cong \triangle CDE$

Question 4

 In the figure, $A B C D$ is a rhombus. Are $\triangle A D C$ and $\triangle A B C$ congruent? What can you say about $\triangle A B D$ and $\triangle B C D$ ?

(IMAGE TO BE ADDED)

Sol: $A D=A B$

$C D=B C$

$A C=A C$

Hence By SSS $\triangle A C D \cong \triangle A B C$

$A D=C D$

$A B=B C$

$B D=B D$

$\triangle A B D \cong \triangle  C B D$ (BY SSS)

Question 5

In this figure, $T S \| P Q$ and $T S=P Q$. Prove that the triangles $P Q R$ and $S T R$ are congruent.

(IMAGE TO BE ADDED)

Sol: $\angle R S T=\angle R P Q$

TS= PQ = 5cm

$\angle R T S=\angle R Q P$ 

(By ASA)

$STR\cong \triangle P Q R$

Question 6

$\triangle P R Q \cong \triangle L M N$. If $P Q=6 \mathrm{~cm}, P R=5 \mathrm{~cm}$ and $\angle P=50^{\circ}$, find $N L$ and $\angle L$ if $L M=5 \mathrm{~cm}$ and $Q R=M N$.

(IMAGE TO BE ADDED)

Sol: $\triangle P R Q \cong \triangle L M N$ (Given )

PR = LM 

PQ = LN =NL = 6cm 

Hence corresponding side and angle of congruent angle are equal 

Question 7

In the diagrams of the following figures. Name the triangle which is congruent to $\triangle A B C$ Keeping the letters in the right order. State the congruence condition also. 

(IMAGE TO BE ADDED)

Question 8

In each of the following name the congruent triangles and state the congruence condition.

(IMAGE TO BE ADDED)