In triangles $ABC$ and $DEF$, $\angle A=\angle D, \angle B=\angle E$ and $AB=EF$. Will the two triangles be congruent? Give reasons for your answer.

In the above figure, $ABCD$ is a square. $P, Q$ and $R$ are points on the sides $AB, BC$ and $CD$ respectively such that $AP=BQ=CR$ and $\angle PQR=90°$. Prove that $△PBQ\cong △QCR$.

In the above figure, $ABCD$ is a square. $P, Q$ and $R$ are points on the sides $AB, BC$ and $CD$ respectively such that $AP=BQ=CR$ and $\angle PQR=90°$. Prove that $PQ=QR$.

In the above figure, $ABCD$ is a square. $P, Q$ and $R$ are points on the sides $AB, BC$ and $CD$ respectively such that $AP=BQ=CR$ and $\angle PQR=90°$. Prove that $\angle PRQ=45°$.

In the adjoining figure, $OA\perp OD, OC\perp OB, OD=OA$ and $OB=OC$. Prove that $AB=CD$.

In the adjoining figure, $PQ\parallel BA$ and $RS\parallel CA$. If $BP=RC$, prove that $△BSR\cong △PQC$.

In the adjoining figure, $PQ\parallel BA$ and $RS\parallel CA$. If $BP=RC$, prove that $BS=PQ$.

In the adjoining figure, $PQ\parallel BA$ and $RS\parallel CA$. If $BP=RC$, prove that $RS=CQ$.

In the adjoining figure, $AB=AC$, $D$ is a point in the interior of $△ABC$ such that $\angle DBC=\angle DCB$. Prove that $AD$ bisects $\angle BAC$ of $△ABC$.