Question

$PQ$ and $RS$ bisect each other at $O$ as shown in the figure. Prove that $PR=QS$.

Answer 1

Step 1: Proving that $∆POR\cong ∆QOS$

In $∆POR$ and $∆QOS$,

$PO=QO$ [ $O$ bisects $PQ$]

$\angle POR=\angle QOS$ [ Vertically Opposite angles ]

$OR=OS$ [ $O$ bisects $RS$]

Therefore, by SAS congruence condition $∆POR\cong ∆QOS$

Step 2: Proving that $PR=QS$

Since corresponding parts of congruent triangles are equal.

$\therefore PR=QS$ [ By C.P.C.T. ]

Hence, proved.