图示为一个菱形 ABCD。 ABQ、PBC 和 DRQ 均为直线，且 AQ = BP。

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完整解法

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.

答案

$AD=AB$ since $ABCD$ is a rhombus.

$\angle DAQ=\angle ABP$ since $AD\parallel BC$ and $P,B,C$ are collinear, while $A,B,Q$ are collinear.

$AQ=BP$ is given.

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

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