if AEC intersects BED at E, and angle B is congruent to Angle D, prove angle A is congruent to angle C

Question

given- AEC intersects BED at E, angle B is congruent to Angle D

prove- angle A is congruent to angle C

 

Answer 1

It surely helps to draw the figure. You will have two triangles, EAD & ECB.

Angles B & D are congruent...that's one angle in each triangle.

At E, there's a pair of congruent vertical angles...that's a second angle in each triangle.

The aforementioned two triangles are congruent, by "AA" and consequently

the third pair of corresponding angles, namely A and C, are congruent.

 

Q.E.D.