The diagram shows a rhombus ABCD. ABQ, PBC and DRQ are straight lines and AQ = BP.

1. State the equal side from the rhombus and the given equal side.

Since $ABCD$ is a rhombus,
$AD=AB.$
Also, it is given that
$AQ=BP.$

2. State the included equal angle and conclude congruence by SAS.

Since $AD\parallel BC$ and $P,B,C$ are collinear, $AD\parallel BP$.

Since $A,B,Q$ are collinear, $AQ$ lies on the same straight line as $AB$.

Hence
$\angle DAQ=\angle ABP.$

Therefore,
$\triangle DQA\cong\triangle APB$
by SAS.