Which statement justifies the given reasons in the geometric proof below?

1. PR bisects ∠QPS.
2. ∠QPR is congruent to ∠RPS.
3. ∠QPS is a right angle.
4. ∠QPS measures _ degrees.
5. ∠QPR measures _ degrees and ∠RPS measures _ degrees, adding up to the measure of ∠QPS.
6. ∠QPR and ∠RPS together form a total of _ degrees.
7. Doubling the measure of ∠RPS gives a total of 90°.
8. Therefore, the measure of ∠RPS is ___ degrees.

a) Definition of a Right Angle
b) Angle Addition Postulate
c) Segment Addition Postulate
d) Distributive Property

The statement that justifies the given reasons in the geometric proof is the Angle Addition Postulate. The proof uses the facts that PR bisects ∠QPS, ∠QPR is congruent to ∠RPS, ∠QPS is a right angle, ∠QPS measures 90 degrees, ∠QPR measures 45 degrees, ∠RPS measures 45 degrees, doubling the measure of ∠RPS gives a total of 90 degrees, and therefore the measure of ∠RPS is 45 degrees.

Explanation:

The statement that justifies the given reasons in the geometric proof is b) Angle Addition Postulate.

PR bisects ∠QPS: This means that the angle ∠QPS is divided into two congruent angles, ∠QPR and ∠RPS.

∠QPR is congruent to ∠RPS: Since PR bisects ∠QPS, ∠QPR and ∠RPS are congruent by definition.

∠QPS is a right angle: This is given in the proof.

∠QPS measures 90 degrees: This is given in the proof.

∠QPR measures 45 degrees and ∠RPS measures 45 degrees: Since ∠QPR and ∠RPS are congruent and their measures add up to the measure of ∠QPS, each angle measures half of 90 degrees, which is 45 degrees.

∠QPR and ∠RPS together form a total of 90 degrees: This is simply the fact that their measures add up to 90 degrees.

Double the measure of ∠RPS gives a total of 90 degrees: This is given in the proof.

Therefore, the measure of ∠RPS is 45 degrees: By doubling the measure of ∠RPS, we get 90 degrees and since the measure of ∠RPS and ∠QPR are equal, each angle measures 45 degrees.