Question

name the postulate that proves each pair of triangles is congruent. list the vertices of the congruent triangle in correct corresponding order. complete the statement below. \\( \triangle a b c \cong \\) by the postulate.

Explanation:

• First, identify the congruent parts. In \(\triangle ABC\) and \(\triangle DFE\), we can see that two sides and the included angle are congruent.
• The Side - Angle - Side (SAS) postulate 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.
• For the vertex order: In \(\triangle ABC\), side \(AB\) corresponds to side \(DF\), angle \(B\) corresponds to angle \(F\), and side \(BC\) corresponds to side \(FE\). So the congruent triangle is \(\triangle DFE\).

Answer:

\(\triangle ABC\cong\triangle DFE\) by the \(SAS\) Postulate.