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6. Given : 23 24, RT ST 3. Prove: HR ES 2. R

6. Given : 23 24, RT ST 3. Prove: HR ES 2. R

Elementary Geometry For College Students, 7e
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
Problem 1CT
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**Problem 6: Given and Proof Structure** **Given:** - \( \angle 3 \cong \angle 4 \) - \( RT \cong ST \) **Prove:** - \( HR \cong ES \) **Diagram Explanation:** The diagram is a geometric figure consisting of two intersecting triangles forming a quadrilateral. Points H, E, R, and S form the vertices, and there is a point T where the diagonals intersect. Angles and segments are labeled as follows: - Angles \( \angle 3 \) and \( \angle 4 \) are congruent. - Segments \( RT \) and \( ST \) are congruent. **Proof Structure:** A flowchart layout is provided for the proof. It consists of five rectangular boxes connected by arrows indicating logical steps. Below each rectangle, there is space for written justifications or statements. The specific proof steps and justifications are not filled in the diagram. This structure is intended for organizing a proof by sequentially verifying geometric properties and congruencies leading to the conclusion that \( HR \cong ES \).
Transcribed Image Text:**Problem 6: Given and Proof Structure** **Given:** - \( \angle 3 \cong \angle 4 \) - \( RT \cong ST \) **Prove:** - \( HR \cong ES \) **Diagram Explanation:** The diagram is a geometric figure consisting of two intersecting triangles forming a quadrilateral. Points H, E, R, and S form the vertices, and there is a point T where the diagonals intersect. Angles and segments are labeled as follows: - Angles \( \angle 3 \) and \( \angle 4 \) are congruent. - Segments \( RT \) and \( ST \) are congruent. **Proof Structure:** A flowchart layout is provided for the proof. It consists of five rectangular boxes connected by arrows indicating logical steps. Below each rectangle, there is space for written justifications or statements. The specific proof steps and justifications are not filled in the diagram. This structure is intended for organizing a proof by sequentially verifying geometric properties and congruencies leading to the conclusion that \( HR \cong ES \).
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