Question

which two triangles are congruent by the sas theorem? complete the congruence statement.

Explanation:

Step1: Recall SAS (Side - Angle - Side) theorem

The SAS theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the triangles

In \(\triangle DBC\) and \(\triangle WXY\), we can observe that:

• In \(\triangle DBC\), we have two sides \(DB\) and \(BC\) and the included - angle \(\angle B\).
• In \(\triangle WXY\), we have two sides \(WX\) and \(XY\) and the included - angle \(\angle X\).

We can see that \(DB = WX\) (single hash mark), \(BC=XY\) (double hash marks), and \(\angle B=\angle X\) (marked with the same arc).

Answer:

\(\triangle DBC\cong\triangle WXY\)