Question

EAB and DCB are two right triangles. The figure has BED≅ BDE. Point B is the midpoint of segment AC. Prove: EAB≅ DCB

Answer 1

we know both triangles are right-triangles, so they must have a 90° angle somewheres.

we also know that B is the midpoint of AC, so the segments of AB = BC, so we know the triangles have that side in common length.

but we also know that the ∡BED = ∡BDE, so the triangles have that angle in common as well.

well, the angles made at the vertex B, namely ∡ABE and ∡CBD, can't be 90°, due to the inclination from the sides E and D, so the right-angles must be at vertices A and D.

∡BAE = ∡BCD.........ANGLE

∡BED = ∡BDE..........ANGLE

AC = BC......................SIDE

so the triangles are congruent by AAS.