Question

In the following, it is known that MPQ, angle 1 = angle 3 and line PR bisects angle QPN. Prove: line MN || line PR

Options:
a. MN is perpendicular to PR
b. MPQ = angle 1 = angle 3 = PRN
c. MPQ = angle 3 = angle 1 = PRN
d. MN is parallel to PR

Answer 1

To prove that line MN is parallel to line PR, we can use the given information about the angles MPQ, 1, and 3.

Step-by-step explanation:

To prove that line MN is parallel to line PR, we need to use the given information that MPQ angle 1 = angle 3 and line PR bisects angle QPN.

Here's the proof:

1. MPQ angle 1 = angle 3 (given)

2. Angle PRN = angle 1 (angle bisector)

3. Angle PRN = angle 3 (substitution from step 1)

4. Therefore, line MN is parallel to line PR (corresponding angles are congruent).