Question

Triangle ABC is congruent to triangle DEF. In triangle ABC, side AB measures 13, side BC measures x+13, and side CA measures 16. In triangle DEF, side DE measures 13, side EF measures 3x−20, and side FD measures 16. What equation would help you to solve for the side length of BC and EF? Explain your reasoning using complete sentences.

Answer 1

Since the triangles are congruent, the sides and angles are the same.

So AB=DE, BC=EF, and AC=DF

Since BC=EF just substitute the given value for each side and solve for x. So you would have this:

x+13=3x-20
2x=33
x=33/2 or 16.5

So BC = EF= 16.5

Answer 2

Actually, BC = EF = 29.5