Question

PR is diagonal of a parallelogram PQRS. Show that $\Delta$ PQR $\cong$ $\Delta$ RSP.

Answer 1

Given that $PQRS$ is a parallelogram.

Hence, $PQ\parallel RS$ and $PS\parallel QR$

We know that, alternate interior angles formed by a line intersecting two parallel lines, are equal.

$\therefore \angle SRP=\angle RPQ$ (Alternate interior angles)

$PR=PR$ (Common)

$\angle SPR=\angle PRQ$ (Alternate interior angles)

According to ASA congruency Criterion

$△PQR\cong △RSP\left[Henceproved\right]$