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Example 2 Using the SAS Congruence Postulate Prove that ASYT = AWYX. Statements Reasons 1. TY = SY = 1. Given 2. Z1 = 2 2. 3. ASYT = AWYX 3.

Example 2 Using the SAS Congruence Postulate Prove that ASYT = AWYX. Statements Reasons 1. TY = SY = 1. Given 2. Z1 = 2 2. 3. ASYT = AWYX 3.

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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### Example 2: Using the SAS Congruence Postulate **Problem Statement:** Prove that \( \triangle SYT \cong \triangle WYX \). #### Diagram Explanation: The diagram shows two triangles, \( \triangle SYT \) and \( \triangle WYX \), sharing a common vertex \( Y \). The line segments \( TY \) and \( WY \) are marked equally with single ticks, indicating they are congruent. Similarly, line segments \( SY \) and \( XY \) are marked with double ticks, indicating their congruence. Angles \( \angle 1 \) and \( \angle 2 \) are also marked to suggest equality. #### Proof Using Statements and Reasons | Statements | Reasons | |---------------------------------------|-------------| | 1. \( \overline{TY} \cong \overline{WY}, \quad \overline{SY} \cong \overline{XY} \) | 1. Given | | 2. \( \angle 1 \cong \angle 2 \) | 2. Vertical Angles are Congruent | | 3. \( \triangle SYT \cong \triangle WYX \) | 3. SAS Congruence Postulate | ### Explanation: - **Step 1:** It is given that the line segments \( TY \) and \( WY \), as well as \( SY \) and \( XY \), are congruent. - **Step 2:** The angles \( \angle 1 \) and \( \angle 2 \) are congruent due to the property of vertical angles. - **Step 3:** By the SAS (Side-Angle-Side) Congruence Postulate, \( \triangle SYT \) is congruent to \( \triangle WYX \) as two sides and the included angle are congruent.
Transcribed Image Text:### Example 2: Using the SAS Congruence Postulate **Problem Statement:** Prove that \( \triangle SYT \cong \triangle WYX \). #### Diagram Explanation: The diagram shows two triangles, \( \triangle SYT \) and \( \triangle WYX \), sharing a common vertex \( Y \). The line segments \( TY \) and \( WY \) are marked equally with single ticks, indicating they are congruent. Similarly, line segments \( SY \) and \( XY \) are marked with double ticks, indicating their congruence. Angles \( \angle 1 \) and \( \angle 2 \) are also marked to suggest equality. #### Proof Using Statements and Reasons | Statements | Reasons | |---------------------------------------|-------------| | 1. \( \overline{TY} \cong \overline{WY}, \quad \overline{SY} \cong \overline{XY} \) | 1. Given | | 2. \( \angle 1 \cong \angle 2 \) | 2. Vertical Angles are Congruent | | 3. \( \triangle SYT \cong \triangle WYX \) | 3. SAS Congruence Postulate | ### Explanation: - **Step 1:** It is given that the line segments \( TY \) and \( WY \), as well as \( SY \) and \( XY \), are congruent. - **Step 2:** The angles \( \angle 1 \) and \( \angle 2 \) are congruent due to the property of vertical angles. - **Step 3:** By the SAS (Side-Angle-Side) Congruence Postulate, \( \triangle SYT \) is congruent to \( \triangle WYX \) as two sides and the included angle are congruent.
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