Question

problem 13: (first taught in lesson 33) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: $overline{be}congoverline{de}$, $angle1congangle aed$, $overline{ec}congoverline{ea}$ prove: $\triangle beccong\triangle dea$

Explanation:

Step1: Identify congruent parts

We are given $\overline{BE}\cong\overline{DE}$, $\angle1\cong\angle AED$, $\overline{EC}\cong\overline{EA}$.

Step2: Recall congruence postulates

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.

Step3: Apply the postulate

In $\triangle BEC$ and $\triangle DEA$, $\overline{BE}$ and $\overline{DE}$ are sides, $\angle1$ (in $\triangle BEC$) and $\angle AED$ (in $\triangle DEA$) are the included angles, and $\overline{EC}$ and $\overline{EA}$ are the other pair of sides. So by SAS, $\triangle BEC\cong\triangle DEA$.

Answer:

Side - Angle - Side (SAS) Congruence Postulate