### Geometry Exploration: Two-Column Proof#### Problem StatementWrite a two-column proof to show that if ∠WXY ≅ ∠ABC, then ∠WXY ≅ ∠ABC.#### Given∠WXY ≅ ∠ABC#### To Prove∠ABC ≅ ∠WXY#### DiagramsThe 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 LayoutHere, 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 Diagrams1. **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.

Given ∠WXY≅∠ABC. The objective is to write a two-column proof to show that ∠ABC≅∠WXY. Concept used :…

Answered: Write a two-column proof to show that…

Math

Geometry

Write a two-column proof to show that if WXY ABC, then WXY = ABC. L W A X Given: WXY ABC Prove: ABC = WXY L L C B Y

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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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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