Given: AB is congruent to AC, CB is congruent to CD Prove: AB times DB = (CB)^2

Question

ABC is a large triangle. BCD is inside that triangle. Point D is between A and B.

Answer 1

angles CDB and CBD are congruent because of the isoceles triangle BCD

 

Likewise,  angles ABC and  BCA are congruent because of isoceles triangle ABC

 

So BCD and BAC are congruent by 180 degree property of triangles

 

Since the corresponding angles are congruent, the triangles are similar

SPECIFICALLY, triangles BCD and CAB are similar

 

The sides are in proportion

 

DB / CB = CB / AB

 

Cross multiplication completes the proof