Question

12 which congruence postulate should be used to prove △abe≅△cda if eb≅ad and m∠adc = 90°? aas congruence postulate sas congruence postulate hl theorem aaa congruence postulate

Explanation:

Step1: Identify given information

We are given $\overline{EB}\cong\overline{AD}$ and $\angle ADC = 90^{\circ}$. Also, in right - angled triangles $\triangle ABE$ and $\triangle CDA$, $\angle ABE=\angle ADC = 90^{\circ}$ (right - angles), and $\angle BAE$ and $\angle DCA$ are non - included angles to the given equal sides, and $\overline{EB}\cong\overline{AD}$ are non - included sides to the right - angles.

Step2: Recall congruence postulates

The AAS (Angle - Angle - Side) congruence postulate 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. Here, we have two right - angles equal, another pair of angles (the non - right angles) and a non - included side equal.

Answer:

D. AAS Congruence Postulate