$PQRS$ 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 $\angle ABD$.

Mention whether the following pair of triangles are congruent by $SAS$ congruence condition or not? State the result in symbolic form.

Mention whether the following pair of triangles are congruent by $SAS$ congruence condition or not? State the result in symbolic form.

Find the measurements of the unknown side or angle marked by small letters in the following pairs of congruent triangles.

Find the measurements of the unknown side or angle marked by small letters in the following pairs of congruent triangles.

Find the measurements of the unknown side or angle marked by small letters in the following pairs of congruent triangles.

In the following figure $AB=AD$ and $\angle BAC=\angle DAC$. Prove that line segment $CA$ bisects $\angle BCD$.