Question

which two triangles are congruent by the aas theorem? complete the congruence statement.
$\triangle square cong \triangle$

Explanation:

Step1: Recall AAS Theorem

AAS (Angle-Angle-Side) states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the triangles are congruent.

Step2: Analyze triangle WXY

In $\triangle WXY$: $\angle X \cong \angle Y$, non-included side $\overline{WX}$ is marked congruent.

Step3: Analyze triangle QRP

In $\triangle QRP$: $\angle R \cong \angle Q$, non-included side $\overline{RP}$ is marked congruent.

Step4: Analyze triangle GHI

In $\triangle GHI$: $\angle G \cong \angle H$, included side $\overline{GI}$ is marked congruent (matches ASA, not AAS).

Step5: Match AAS criteria

$\triangle WXY$ has two congruent angles and a non-included congruent side; $\triangle QRP$ has two congruent angles and a corresponding non-included congruent side, fitting AAS.

Answer:

$\triangle WXY \cong \triangle QRP$