Question

4 fill in the blank 9 points
4.
$\triangle pqs \cong \triangle \square$ by $\square$

Explanation:

Step1: Identify congruent sides

We know $SP = RQ$ (marked congruent), $SQ = QS$ (common side, reflexive property). Also, since $PQ \parallel SR$ and $SP \parallel RQ$, this is a parallelogram, so $PQ = SR$.

Step2: Match congruent triangles

For $\triangle PQS$, the corresponding congruent triangle is $\triangle RSQ$, as all three pairs of sides are congruent: $SP=RQ$, $PQ=SR$, $SQ=QS$.

Step3: Determine congruence rule

Since three sides of one triangle are congruent to three sides of the other triangle, we use the Side-Side-Side (SSS) congruence criterion.

Answer:

$\triangle PQS \cong \triangle RSQ$ by SSS