Question

(a) problem 12: (first taught in lesson 33)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: $overline{be}congoverline{de}$, $angle2congangle bea$, $overline{ea}congoverline{ec}$
prove: $\triangle beacong\triangle dec$

Explanation:

Step1: Identify corresponding parts

We have $\overline{BE}\cong\overline{DE}$ (side), $\angle2\cong\angle BEA$ (angle), $\overline{EA}\cong\overline{EC}$ (side).

Step2: Recall congruence postulates

The 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. Here, in $\triangle BEA$ and $\triangle DEC$, we have two pairs of congruent sides and the included angles between them are congruent, so we can use the SAS postulate to prove $\triangle BEA\cong\triangle DEC$.

Answer:

Side - Angle - Side (SAS) Congruence Postulate