Question

Given: Line PM is congruent to line QM, line MN bisects angle PMQ

Prove: Angle MNP is congruent to Angle MNQ

Answer 1

So, line PM is congruent to line QM, because it is given.
Segment MN is an angle bisector. The definition of an angle bisector is a line or line segment that divides an angle into two equal parts, so Segment MN is congruent to segment MN due to the reflexive property, which states that a number is always equal to itself.

Thus, triangle QMN is congruent to triangle PMN due to the Side-Angle-Side Theorem (SAS).

Now, because congruent parts of corresponding triangles are congruent (CPCTC),