Proving Triangle Congruence

Question

Prove: Triangle CBD is congruent to Triangle CAE

 

Given: angle A is congruent to angle B, Point C is the midpoint of segment AB

 

Answer 1

I think that the probleM's figure has to be as follows.

 

Draw Triangle ABD.  Label midpoint of AB as C.  Draw line segment CD.

 

AC = BC (because C is midpoint of AB, given)

Angle A = angle B(given; congruence is same as equality, for angles)

CD = CD(reflexive property of equality; CD is a side common to two triangles, ΔACD and ΔBCD.

ΔACD ≅ ΔBCD  (ASA)