Question

In this diagram WQ = 1/2 AC. One way to prove this is true is to draw a line through B such that BD is congruent to AC. Then prove triangle ABC is congruent to triangle DCB, and use corresponding parts of the two triangles. Explain why triangle ABC is congruent to triangle DCB.

Answer 1

BD = AC (given)

BD || AC (given)

W is the midpoint of AB (given)

Q is the midpoint of BC (given)

AW = WB (definition of midpoint)

BQ = QC (definition of midpoint)

Angle BCA = Angle DBC (alternate interior angles are congruent)

∆BCA = ∆DBC (SAS)

Angle ABC = Angle DCB (CPCTC)

∆ABC = ∆DCB (SAS)