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If m 24 = m 25, then rlls. Summarize the postulate or theorem that makes this a true statement. r S

If m 24 = m 25, then rlls. Summarize the postulate or theorem that makes this a true statement. r S

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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### Understanding Parallel Lines through Corresponding Angles **Statement:** If \( m \angle 4 = m \angle 5 \), then \( r \parallel s \). Summarize the postulate or theorem that makes this a true statement. **Diagram Explanation:** The diagram shows two lines, \( r \) and \( s \), and a transversal \( l \) that intersects them. Four angles are formed at the intersections marked with numbers. Angles 4 and 5 are shown as corresponding angles. **Summary of Theorem:** The statement is based on the Corresponding Angles Postulate or Theorem. This postulate/theorem states that if two lines are cut by a transversal, then each pair of corresponding angles are equal if and only if the lines are parallel. **Conclusion:** In this scenario, since \( m \angle 4 = m \angle 5 \), we can deduce that lines \( r \) and \( s \) must be parallel, that is, \( r \parallel s \). This relationship between corresponding angles and parallel lines provides a foundational concept in understanding geometric properties and proofs involving parallelism.
Transcribed Image Text:### Understanding Parallel Lines through Corresponding Angles **Statement:** If \( m \angle 4 = m \angle 5 \), then \( r \parallel s \). Summarize the postulate or theorem that makes this a true statement. **Diagram Explanation:** The diagram shows two lines, \( r \) and \( s \), and a transversal \( l \) that intersects them. Four angles are formed at the intersections marked with numbers. Angles 4 and 5 are shown as corresponding angles. **Summary of Theorem:** The statement is based on the Corresponding Angles Postulate or Theorem. This postulate/theorem states that if two lines are cut by a transversal, then each pair of corresponding angles are equal if and only if the lines are parallel. **Conclusion:** In this scenario, since \( m \angle 4 = m \angle 5 \), we can deduce that lines \( r \) and \( s \) must be parallel, that is, \( r \parallel s \). This relationship between corresponding angles and parallel lines provides a foundational concept in understanding geometric properties and proofs involving parallelism.
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