Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
### Geometry Exploration: Two-Column Proof #### Problem Statement Write a two-column proof to show that if ∠WXY ≅ ∠ABC, then ∠WXY ≅ ∠ABC. #### Given ∠WXY ≅ ∠ABC #### To Prove ∠ABC ≅ ∠WXY #### Diagrams The image includes two diagrams: 1. **Diagram 1 (Left Side)** - Consists of points W, X, and Y. - Triangle WXY is formed with the angle at point X labeled as ∠WXY. 2. **Diagram 2 (Right Side)** - Consists of points A, B, and C. - Triangle ABC is formed with the angle at point B labeled as ∠ABC. #### Proof Layout Here, we outline the two-column proof required to demonstrate the statement. | **Statement** | **Reason** | |-------------------------|----------------------------------| | 1. ∠WXY ≅ ∠ABC | Given | | 2. ∠ABC ≅ ∠WXY | Symmetric Property of Congruence | This simple two-step proof utilizes the given information and the symmetric property of congruence, which states that if one angle is congruent to another, the second angle is also congruent to the first. #### Explanation of Diagrams 1. **Diagram 1:** - The points W, X, and Y form a triangle with the vertex at X. - An arrow starting from X points towards W and Y, indicating the formation of ∠WXY. 2. **Diagram 2:** - The points A, B, and C form a triangle with the vertex at B. - An arrow starting from B points towards A and C, indicating the formation of ∠ABC. By proving that the angles are congruent through the symmetric property, we validate the assertion of the problem statement effectively.
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Transcribed Image Text:### Geometry Exploration: Two-Column Proof #### Problem Statement Write a two-column proof to show that if ∠WXY ≅ ∠ABC, then ∠WXY ≅ ∠ABC. #### Given ∠WXY ≅ ∠ABC #### To Prove ∠ABC ≅ ∠WXY #### Diagrams The image includes two diagrams: 1. **Diagram 1 (Left Side)** - Consists of points W, X, and Y. - Triangle WXY is formed with the angle at point X labeled as ∠WXY. 2. **Diagram 2 (Right Side)** - Consists of points A, B, and C. - Triangle ABC is formed with the angle at point B labeled as ∠ABC. #### Proof Layout Here, we outline the two-column proof required to demonstrate the statement. | **Statement** | **Reason** | |-------------------------|----------------------------------| | 1. ∠WXY ≅ ∠ABC | Given | | 2. ∠ABC ≅ ∠WXY | Symmetric Property of Congruence | This simple two-step proof utilizes the given information and the symmetric property of congruence, which states that if one angle is congruent to another, the second angle is also congruent to the first. #### Explanation of Diagrams 1. **Diagram 1:** - The points W, X, and Y form a triangle with the vertex at X. - An arrow starting from X points towards W and Y, indicating the formation of ∠WXY. 2. **Diagram 2:** - The points A, B, and C form a triangle with the vertex at B. - An arrow starting from B points towards A and C, indicating the formation of ∠ABC. By proving that the angles are congruent through the symmetric property, we validate the assertion of the problem statement effectively.
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