Question

which two triangles are congruent by the aas theorem? complete the congruence statement.
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Explanation:

Step1: Recall AAS Congruence

AAS (Angle - Angle - Side) congruence theorem 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, then the two triangles are congruent.

Step2: Analyze the Triangles

• For \(\triangle HGI\) and \(\triangle WYX\):
• Let's check the angles and sides. In \(\triangle HGI\), we have two marked angles (at \(H\) and \(I\)) and a marked side ( \(HG\)). In \(\triangle WYX\), we have two marked angles (at \(Y\) and \(X\)) and a marked side ( \(WY\)). The angles and the non - included side seem to match the AAS criteria.
• For \(\triangle CDE\), the marked side and angles do not match the pattern of \(\triangle HGI\) or \(\triangle WYX\) in a way that satisfies AAS with either of the other two triangles.

By comparing the angle markings (two angles) and the side markings (non - included side) of the triangles, we can see that \(\triangle HGI\) and \(\triangle WYX\) satisfy the AAS congruence theorem. So the congruence statement is \(\triangle HGI\cong\triangle WYX\) (or \(\triangle WYX\cong\triangle HGI\)).

Answer:

\(\triangle HGI\cong\triangle WYX\) (or \(\triangle WYX\cong\triangle HGI\))