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3. In the diagram, ZX=ZY. W Prove: mn X Y Statements 1. LX= LY 2.LY= LZ N Reasons 1. Given 2. Vertical angle theorem - m n

3. In the diagram, ZX=ZY. W Prove: mn X Y Statements 1. LX= LY 2.LY= LZ N Reasons 1. Given 2. Vertical angle theorem - m n

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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Answer the question ( it’s not the first option Corresponding Angles Postulate)
**Diagram Explanation:** The diagram shows angles \( \angle X \), \( \angle Y \), and \( \angle Z \) formed by lines \( m \) and \( n \) intersected by a transversal. **Proof:** Given: \( \angle X \cong \angle Y \) **To Prove:** \( m \parallel n \) **Statements and Reasons:** 1. \( \angle X \cong \angle Y \) - **Reason:** Given 2. \( \angle Y \cong \angle Z \) - **Reason:** Vertical angle theorem 3. \( \angle X \cong \angle Z \) - **Reason:** Transitive property of congruence 4. \( m \parallel n \) - **Reason:** ____________________________ **Question:** Which reason completes the proof? - \( A \) Corresponding Angles Postulate - \( B \) Alternate Exterior Angles Theorem - \( C \) Converse of the Corresponding Angles Postulate - \( D \) Converse of the Alternate Exterior Angles Theorem The correct answer to complete the proof is option \( C \), the **Converse of the Corresponding Angles Postulate**, which allows us to conclude that the lines \( m \) and \( n \) are parallel given that the corresponding angles are congruent.
Transcribed Image Text:**Diagram Explanation:** The diagram shows angles \( \angle X \), \( \angle Y \), and \( \angle Z \) formed by lines \( m \) and \( n \) intersected by a transversal. **Proof:** Given: \( \angle X \cong \angle Y \) **To Prove:** \( m \parallel n \) **Statements and Reasons:** 1. \( \angle X \cong \angle Y \) - **Reason:** Given 2. \( \angle Y \cong \angle Z \) - **Reason:** Vertical angle theorem 3. \( \angle X \cong \angle Z \) - **Reason:** Transitive property of congruence 4. \( m \parallel n \) - **Reason:** ____________________________ **Question:** Which reason completes the proof? - \( A \) Corresponding Angles Postulate - \( B \) Alternate Exterior Angles Theorem - \( C \) Converse of the Corresponding Angles Postulate - \( D \) Converse of the Alternate Exterior Angles Theorem The correct answer to complete the proof is option \( C \), the **Converse of the Corresponding Angles Postulate**, which allows us to conclude that the lines \( m \) and \( n \) are parallel given that the corresponding angles are congruent.
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