Question

What is the reason for Statement 2 of the two-column proof?

Answer 1

The reason for statement 2 is: Angle Bisector Postulate. By definition, an angle bisector is a ray that is drawn at the center of the angle. When an angle bisector is drawn, it divides the angle into two equal parts. So, the individual angles ∠RPQ and ∠QPS must be equal.

Answer 2

We have been given that PQ bisects $\angle RPS$. In the second statement of the given two-column proof, the statement is $\angle RPQ\cong\angle QPS$.

This implies that the two angles formed by bisection of angle $\angle RPS$ by the line PQ are equal. We know that the reason for this is simple. It is the definition of bisection of an angle that the two smaller angles formed will be equal to each other.

Therefore, the reason for statement 2 of the given two column proof is c) Definition of bisect