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Certainly! Here is the transcription with a detailed explanation suitable for an educational website: --- **Geometric Proof Using Supplementary Angles** **Problem Statement:** Given: - ∠2 and ∠3 are supplementary. - ∠2 and ∠3 are a linear pair. **Prove:** - ∠1 ≅ ∠3 **Proof:** 1. ∠2 and ∠3 are supplementary. 2. ∠2 and ∠3 are a linear pair. By the Linear Pair Postulate, ∠2 and ∠3 are supplementary. 3. ∠1 and ∠2 are supplementary. 4. By the Congruent Supplements Theorem, ∠1 ≅ ∠3. **Bank (Choose the Appropriate Terms):** - Reflexive Property of Angle Congruence - Congruent Supplements Theorem - Linear Pair Postulate **Diagram Explanation:** - The diagram shows two intersecting lines, forming angles at the intersection. - Angles are labeled as 1, 2, and 3. - Angles ∠2 and ∠3 form a linear pair. **Notes:** The diagram illustrates the relationship between angles that are supplementary and part of a linear pair. In the given proof, it uses the Linear Pair Postulate, which states that if two angles form a linear pair, they are supplementary (i.e., their measures add up to 180°). The Congruent Supplements Theorem further states that if two angles are supplementary to the same angle, they are congruent to each other. --- This explanation is designed to guide students through understanding the geometric relationships and theorems involved in the proof.

Certainly! Here is the transcription with a detailed explanation suitable for an educational website: --- **Geometric Proof Using Supplementary Angles** **Problem Statement:** Given: - ∠2 and ∠3 are supplementary. - ∠2 and ∠3 are a linear pair. **Prove:** - ∠1 ≅ ∠3 **Proof:** 1. ∠2 and ∠3 are supplementary. 2. ∠2 and ∠3 are a linear pair. By the Linear Pair Postulate, ∠2 and ∠3 are supplementary. 3. ∠1 and ∠2 are supplementary. 4. By the Congruent Supplements Theorem, ∠1 ≅ ∠3. **Bank (Choose the Appropriate Terms):** - Reflexive Property of Angle Congruence - Congruent Supplements Theorem - Linear Pair Postulate **Diagram Explanation:** - The diagram shows two intersecting lines, forming angles at the intersection. - Angles are labeled as 1, 2, and 3. - Angles ∠2 and ∠3 form a linear pair. **Notes:** The diagram illustrates the relationship between angles that are supplementary and part of a linear pair. In the given proof, it uses the Linear Pair Postulate, which states that if two angles form a linear pair, they are supplementary (i.e., their measures add up to 180°). The Congruent Supplements Theorem further states that if two angles are supplementary to the same angle, they are congruent to each other. --- This explanation is designed to guide students through understanding the geometric relationships and theorems involved in the proof.

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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Certainly! Here is the transcription with a detailed explanation suitable for an educational website: --- **Geometric Proof Using Supplementary Angles** **Problem Statement:** Given: - ∠2 and ∠3 are supplementary. - ∠2 and ∠3 are a linear pair. **Prove:** - ∠1 ≅ ∠3 **Proof:** 1. ∠2 and ∠3 are supplementary. 2. ∠2 and ∠3 are a linear pair. By the Linear Pair Postulate, ∠2 and ∠3 are supplementary. 3. ∠1 and ∠2 are supplementary. 4. By the Congruent Supplements Theorem, ∠1 ≅ ∠3. **Bank (Choose the Appropriate Terms):** - Reflexive Property of Angle Congruence - Congruent Supplements Theorem - Linear Pair Postulate **Diagram Explanation:** - The diagram shows two intersecting lines, forming angles at the intersection. - Angles are labeled as 1, 2, and 3. - Angles ∠2 and ∠3 form a linear pair. **Notes:** The diagram illustrates the relationship between angles that are supplementary and part of a linear pair. In the given proof, it uses the Linear Pair Postulate, which states that if two angles form a linear pair, they are supplementary (i.e., their measures add up to 180°). The Congruent Supplements Theorem further states that if two angles are supplementary to the same angle, they are congruent to each other. --- This explanation is designed to guide students through understanding the geometric relationships and theorems involved in the proof.
Transcribed Image Text:Certainly! Here is the transcription with a detailed explanation suitable for an educational website: --- **Geometric Proof Using Supplementary Angles** **Problem Statement:** Given: - ∠2 and ∠3 are supplementary. - ∠2 and ∠3 are a linear pair. **Prove:** - ∠1 ≅ ∠3 **Proof:** 1. ∠2 and ∠3 are supplementary. 2. ∠2 and ∠3 are a linear pair. By the Linear Pair Postulate, ∠2 and ∠3 are supplementary. 3. ∠1 and ∠2 are supplementary. 4. By the Congruent Supplements Theorem, ∠1 ≅ ∠3. **Bank (Choose the Appropriate Terms):** - Reflexive Property of Angle Congruence - Congruent Supplements Theorem - Linear Pair Postulate **Diagram Explanation:** - The diagram shows two intersecting lines, forming angles at the intersection. - Angles are labeled as 1, 2, and 3. - Angles ∠2 and ∠3 form a linear pair. **Notes:** The diagram illustrates the relationship between angles that are supplementary and part of a linear pair. In the given proof, it uses the Linear Pair Postulate, which states that if two angles form a linear pair, they are supplementary (i.e., their measures add up to 180°). The Congruent Supplements Theorem further states that if two angles are supplementary to the same angle, they are congruent to each other. --- This explanation is designed to guide students through understanding the geometric relationships and theorems involved in the proof.
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