Identify the pairs of congruent triangles from the following and give reason in support of your answer. Write the congruence in symbolic form.

Identify the pairs of congruent triangles from the following and give reason in support of your answer. Write the congruence in symbolic form.

In $∆$ABC,altitude AD bisects BC.Prove that $∆$ADB$\cong$$∆$ADC.write equal pair of sides of these two traingles.

In the given figure, $PQ= SR \text{and }PQ\parallel SR$. Prove that $∆PSR\cong ∆RQP$. Is $PS= QR$?

In the given figure, $AD$ is the bisector of $\angle A$ of $∆ABC$ in which $AB= AC$. Prove that angles opposite to equal sides are equal.

In the given figure, $ABCD$ is a quadrilateral and $AC$ is a diagonal. Prove that $△ABC\cong △CDA.$ Is $AD\parallel CB?$

In the given figure $l\parallel m$ and M is the midpoint of the line segment $PQ$. Prove using $ASA$ criteria that $M$ is also the midpoint of $RS$

In the given figure, P is any point on the bisector of $\angle AOB.$ If $PM\perp OA \text{and} PN\perp OB.$ Prove that $PM=PN$.

A quadrilateral $ABCD$ is such that the diagonal $AC$ bisects each of the angles $BAD \text{and} BCD$ . Prove that$AC$  bisects BD at right angles.