Question

given: \\( \angle a \cong \angle b, \overline{ad} \cong \overline{be} \\) prove: \\( \triangle aed \cong \triangle bed \\) what is the
eason\ for step 4 of the proof?

Explanation:

Step1: Analyze given information

We are given that \( \angle A=\angle B\) and \( \overline{AD}\cong\overline{BC}\). Also, \( \angle AED\) and \( \angle BEC\) are vertical angles (by Vertical Angles Theorem).

Step2: Recall triangle - congruence theorems

• AAS (Angle - Angle - Side): 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.
• In \( \triangle AED\) and \( \triangle BEC\), we have \( \angle A=\angle B\) (given), \( \angle AED=\angle BEC\) (vertical angles are congruent), and \( \overline{AD}\cong\overline{BC}\) (given).

Answer:

AAS ≅ Thrm