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)
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