Question

given: ∠b and ∠d are right angles.
overline{ae} bisects overline{bd}
prove: △abc ≅ △edc

Explanation:

Step1: Vertical angles are equal

$\angle ACB=\angle ECD$

Step2: AAS congruence criterion

Since $\angle B = \angle D$ (right angles), $\angle ACB=\angle ECD$, and $AE$ bisects $BD$ so $BC = DC$ (by the property of angle - bisector and right - angled triangles, we can get the side - angle - side relationship. In right - angled triangles with two angles equal ($\angle B=\angle D$, $\angle ACB = \angle ECD$) and a non - included side equal (because of the angle - bisector property in right - angled triangles, we can use the AAS (Angle - Angle - Side) congruence criterion). So $\triangle ABC\cong\triangle EDC$.

Answer:

$\triangle ABC\cong\triangle EDC$