Welcome to our educational website! Today, we'll analyze a geometry problem involving triangle congruence. **Problem Statement:**We have the following geometric figure, which includes triangle XYZ with a point W on line segment XZ such that WZ passes through to point Y, creating two smaller triangles: ΔXWZ and ΔYWZ.Based on the provided conditions:1. Line segment $ \overline{WZ} $ bisects $ \angle XZY $2. $ \angle X \cong \angle Y $We are asked which method of triangle congruence can be used to prove that $ \triangle XWZ \cong \triangle YWZ $.**Options:**- SSS (Side-Side-Side)- AAA (Angle-Angle-Angle)- SAS (Side-Angle-Side)- AAS (Angle-Angle-Side)**Detailed Explanation of the Diagram:**- The diagram consists of a large triangle $ \triangle XZY $ with a line segment $ \overline{WZ} $ drawn from point $ W $ on side $ \overline{XZ} $ to point $ Z $ and extended to point $ Y $, forming two smaller triangles: ΔXWZ and ΔYWZ.- $ \overline{WZ} $ is a common side of both triangles ΔXWZ and ΔYWZ.Given these conditions, the method to prove the congruence can be identified as follows:1. $ \overline{WZ} $ is a common side for both triangles.2. $ \angle X \cong \angle Y $ means that the angles at points X and Y are equal.3. Since $ \overline{WZ} $ bisects $ \angle XZY $, the two resulting angles $ \angle XWZ $ and $ \angle YWZ $ are equal.Therefore, we have:- An angle ($ \angle X \cong \angle Y $)- A side ($ \overline{WZ} $ common)- An angle ($ \angle XWZ \cong \angle YWZ $)This corresponds to the Angle-Angle-Side (AAS) method of proving triangle congruence.**Correct Answer:**- AAS

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Answered: wz bisects 2XZY and 2X = ZY . Which…

Math

Geometry

wz bisects 2XZY and 2X = ZY . Which choice of method can be used to prove AXWZ = 4YWZ ?

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

Welcome to our educational website! Today, we'll analyze a geometry problem involving triangle congruence.

**Problem Statement:**

We have the following geometric figure, which includes triangle XYZ with a point W on line segment XZ such that WZ passes through to point Y, creating two smaller triangles: ΔXWZ and ΔYWZ.

Based on the provided conditions:
1. Line segment $ \overline{WZ} $ bisects $ \angle XZY $
2. $ \angle X \cong \angle Y $

We are asked which method of triangle congruence can be used to prove that $ \triangle XWZ \cong \triangle YWZ $.

**Options:**
- SSS (Side-Side-Side)
- AAA (Angle-Angle-Angle)
- SAS (Side-Angle-Side)
- AAS (Angle-Angle-Side)

**Detailed Explanation of the Diagram:**

- The diagram consists of a large triangle $ \triangle XZY $ with a line segment $ \overline{WZ} $ drawn from point $ W $ on side $ \overline{XZ} $ to point $ Z $ and extended to point $ Y $, forming two smaller triangles: ΔXWZ and ΔYWZ.
- $ \overline{WZ} $ is a common side of both triangles ΔXWZ and ΔYWZ.

Given these conditions, the method to prove the congruence can be identified as follows:

1. $ \overline{WZ} $ is a common side for both triangles.
2. $ \angle X \cong \angle Y $ means that the angles at points X and Y are equal.
3. Since $ \overline{WZ} $ bisects $ \angle XZY $, the two resulting angles $ \angle XWZ $ and $ \angle YWZ $ are equal.

Therefore, we have:
- An angle ($ \angle X \cong \angle Y $)
- A side ($ \overline{WZ} $ common)
- An angle ($ \angle XWZ \cong \angle YWZ $)

This corresponds to the Angle-Angle-Side (AAS) method of proving triangle congruence.

**Correct Answer:**
- AAS

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