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1. Describe the relationship between angle 1 and angle 3. Are they congruent or supplementary? How do you know? Use appropriate vocabulary.

1. Describe the relationship between angle 1 and angle 3. Are they congruent or supplementary? How do you know? Use appropriate vocabulary.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...
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### Geometry Exercise - Identifying Angle Relationships **Question:** 1. Describe the relationship between angle 1 and angle 3. Are they congruent or supplementary? How do you know? Use appropriate vocabulary. **Diagram Explanation:** The given diagram features two parallel lines \( a \) and \( b \), intersected by a transversal. The transversal creates several angles, labeled as follows: - Angle 1 (above line \( a \) on the left side of the transversal) - Angle 2 (below line \( a \), immediately next to angle 1, on the right side of the transversal) - Angle 3 (below line \( b \) on the left side of the transversal) - Angle 4 (below line \( b \), immediately next to angle 3, on the right side of the transversal) **Analysis:** Angles 1 and 3 are corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines, and they occupy the same relative position at each intersection. According to the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. Therefore, **angle 1 and angle 3 are congruent**. This means they have equal measures.
Transcribed Image Text:### Geometry Exercise - Identifying Angle Relationships **Question:** 1. Describe the relationship between angle 1 and angle 3. Are they congruent or supplementary? How do you know? Use appropriate vocabulary. **Diagram Explanation:** The given diagram features two parallel lines \( a \) and \( b \), intersected by a transversal. The transversal creates several angles, labeled as follows: - Angle 1 (above line \( a \) on the left side of the transversal) - Angle 2 (below line \( a \), immediately next to angle 1, on the right side of the transversal) - Angle 3 (below line \( b \) on the left side of the transversal) - Angle 4 (below line \( b \), immediately next to angle 3, on the right side of the transversal) **Analysis:** Angles 1 and 3 are corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines, and they occupy the same relative position at each intersection. According to the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. Therefore, **angle 1 and angle 3 are congruent**. This means they have equal measures.
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