Given: line AC bisects angle BAD. Line AC bisects angle BCD. Prove: Angle B is congruent to Angle B

Question

I need the proofs and reasons.

Answer 1

We have formed two triangles, BAC and DAC. They share side AC. They also share equality of the two angles that are bisected, so the triangles are congruent by ASA. Thus the corresponding B and D are equal by corresponding parts of congruent triangles.