Monica Capoor Solutions for Exercise 3: Exercise 13.2

By applying $SSS$ congruency rule in the following figure, state whether they are congruent or not. Write the result in symbolic form.

The triangles in the following pairs are congruent by the $SSS$ congruence rule. Write the congruence of each pair in symbolic form.

The triangles in the following pairs are congruent by the $SSS$ congruence rule. Write the congruence of each pair in symbolic form.

In the following figure $AB=DC$ and $BC=AD$. Is $△ABC\cong △CDA$? Justify your answer.

$△ABC$ is an isosceles triangle in which $AB=AC$. $D$ is the mid point of $BC$. Prove that $△ABD\cong △ACD$. If $\angle B=\left(3x+10\right)°$ and $\angle C=70°$, find the value of $x$.

$PQRS$ is a square whose diagonal $PR$ is joined. Prove that $△PQR\cong △PSR$. 

In the following figure, $AB=DC$ and $CA=BD$. Prove that $△ABC\cong △DCB$.

In the following figure, $△ABC$ and $△DBC$ are both isosceles triangles on common base $BC$ such that $A$ and $D$ lie on the same side of $BC$. Prove that $△ADB\cong △ADC$. If $\angle BAC=40°$ and $\angle BDC=100°$, find the measure of $\angle ABD$.