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Use the diagram at the right for 25 and 26. 26. Given: CD || EF Name a pair of congruent angles and state the reason why. 2 E CD || EF 27. Given: Name a pair of supplementary angles and state the reason why.

Use the diagram at the right for 25 and 26. 26. Given: CD || EF Name a pair of congruent angles and state the reason why. 2 E CD || EF 27. Given: Name a pair of supplementary angles and state the reason why.

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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**Use the diagram at the right for 25 and 26.** **26. Given: \( \overline{CD} \parallel \overline{EF} \)** - **Name a pair of congruent angles and state the reason why.** **27. Given: \( \overline{CD} \parallel \overline{EF} \)** - **Name a pair of supplementary angles and state the reason why.** --- **Diagram Explanation:** The diagram features a triangle with a vertical line \( \overline{CD} \) and a horizontal line \( \overline{EF} \) parallel to each other. Lines \( \overline{CD} \) and \( \overline{EF} \) intersect a third line. The angles formed at the intersection of these lines are labeled 1, 2, 3 at point C and 4, 5 at point F respectively. 1. **Angles Formed:** - Angle 1 is formed by the extension of line \( \overline{CD} \). - Angle 2 and 3 are interior angles between lines \( \overline{CD} \) and the transversal. - Angles 4 and 5 are likewise formed between \( \overline{EF} \) and the transversal. 2. **Parallel Line Properties:** - Since \( \overline{CD} \parallel \overline{EF} \), angle relationships such as corresponding angles, alternate interior angles, and supplementary angles can be identified. This setup allows for identifying congruent and supplementary angles based on these geometric principles.
Transcribed Image Text:**Use the diagram at the right for 25 and 26.** **26. Given: \( \overline{CD} \parallel \overline{EF} \)** - **Name a pair of congruent angles and state the reason why.** **27. Given: \( \overline{CD} \parallel \overline{EF} \)** - **Name a pair of supplementary angles and state the reason why.** --- **Diagram Explanation:** The diagram features a triangle with a vertical line \( \overline{CD} \) and a horizontal line \( \overline{EF} \) parallel to each other. Lines \( \overline{CD} \) and \( \overline{EF} \) intersect a third line. The angles formed at the intersection of these lines are labeled 1, 2, 3 at point C and 4, 5 at point F respectively. 1. **Angles Formed:** - Angle 1 is formed by the extension of line \( \overline{CD} \). - Angle 2 and 3 are interior angles between lines \( \overline{CD} \) and the transversal. - Angles 4 and 5 are likewise formed between \( \overline{EF} \) and the transversal. 2. **Parallel Line Properties:** - Since \( \overline{CD} \parallel \overline{EF} \), angle relationships such as corresponding angles, alternate interior angles, and supplementary angles can be identified. This setup allows for identifying congruent and supplementary angles based on these geometric principles.
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