Complete the following flowchart proofs. Given: ZQPR = ZSPR ZQ = ZS 1. Prove: AQPR = ASPR 5.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Complete the following flowchart proofs.**

1. **Given:**
   - \( \angle QPR \equiv \angle SPR \)
   - \( \angle Q \equiv \angle S \)

   **Prove:**
   - \( \triangle QPR \equiv \triangle SPR \)

**Diagram Explanation:**
- A triangle \( \triangle PQR \) is formed with points Q, R, S, and P. The triangle shows lines connecting P to Q and S, with R being a point on line PS.

**Flowchart:**
- There are three rectangular boxes arranged vertically on the left side that need to be filled with statements or reasons that lead to the proof.
- Arrows from these boxes point to a single rectangular box on the right side, which will contain the conclusion of the proof that \( \triangle QPR \equiv \triangle SPR \).

This proof needs to establish congruence using the given angle congruencies and appropriate theorems in geometry such as Angle-Side-Angle (ASA), Side-Angle-Side (SAS), or others.
Transcribed Image Text:**Complete the following flowchart proofs.** 1. **Given:** - \( \angle QPR \equiv \angle SPR \) - \( \angle Q \equiv \angle S \) **Prove:** - \( \triangle QPR \equiv \triangle SPR \) **Diagram Explanation:** - A triangle \( \triangle PQR \) is formed with points Q, R, S, and P. The triangle shows lines connecting P to Q and S, with R being a point on line PS. **Flowchart:** - There are three rectangular boxes arranged vertically on the left side that need to be filled with statements or reasons that lead to the proof. - Arrows from these boxes point to a single rectangular box on the right side, which will contain the conclusion of the proof that \( \triangle QPR \equiv \triangle SPR \). This proof needs to establish congruence using the given angle congruencies and appropriate theorems in geometry such as Angle-Side-Angle (ASA), Side-Angle-Side (SAS), or others.
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