We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
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.
Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
