In the diagram, $ABCD$ is a parallelogram. The points $P$ and $Q$ lie on the diagonal $AC$ s

Question

In the diagram, $ABCD$ is a parallelogram. The points $P$ and $Q$ lie on the diagonal $AC$ such that $\angle AQD = \angle BPC = 90{}^\circ$. Prove that $\Delta ADQ$ is congruent to $\Delta CBP$. Name another pair of congruent triangles.

Accepted Answer

$\text{(i)}\ \triangle ADQ\equiv\triangle CBP\text{ (AAS)}$ $\text{(ii)}\ \triangle QDC\equiv\triangle PBA\text{ (SSS)}$

Congruence Proofs within Parallelograms: A Study of \(\triangle ADQ\) and \(\triangle CBP\)

Congruence Proofs within Parallelograms: A Study of \(\triangle ADQ\) and \(\triangle CBP\)

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