Question

what triangle congruence theorem could you use to prove triangle ade is congruent to triangle cde?
side - angle - side triangle congruence
angle - side - angle triangle congruence
side - side - side triangle congruence
side - side - angle triangle congruence.

Explanation:

Step1: Identify vertical angles

$\angle AED=\angle BEC$ (vertical angles are equal).

Step2: Analyze given equal sides

$AE = CE$ (given), and assume $DE = BE$ (if not given, but from the figure's symmetry - if we consider the intersection at $E$ and the markings).

Step3: Analyze given angles

$\angle A=\angle C$ (given).

Answer:

Angle - Side - Angle Triangle Congruence.