Prove the Following:

Question

A, B, and C lie in plane E. P and Q are on opposite side of E. Given that PB = QB, A is the midpoint of segment PQ, and angle BPC is congruent to angle BQC, prove that segment PQ is perpendicular to segment AC.

Answer 1

From the given midpoint, PA=QA.

PB=QB is given and BA=AB by reflexive.

So then triangle PAB is congruent to triangle

QAB by SSS.

Angle PAB = angle QAB by CPCTC, AND they

are linear pair, which means they are both

right angles.

As a result, Angles PAC and QAC are also

right angles since they are vertical to

QAB and PAB.

Therefore line PQ is perpendicular to AC