Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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![### Corresponding Angles in Parallel Lines
**Question 10:** Which pairs of angles are corresponding angles?
#### Diagram Description
The image provides a diagram featuring two sets of parallel lines intersected by a transversal. The angles at the intersection points are labeled from 1 to 16. The lines and angles are arranged as follows:
1. The first set of parallel lines and the transversal create angles 1 through 8.
2. The second set of parallel lines and the same transversal create angles 9 through 16.
#### Intersection Points
**First Intersection:**
- Top left of the diagram: Angles 1, 2, 3, and 4.
- Top right of the diagram: Angles 5, 6, 7, and 8.
**Second Intersection:**
- Bottom left of the diagram: Angles 9, 10, 11, and 12.
- Bottom right of the diagram: Angles 13, 14, 15, and 16.
#### Important Concepts - Corresponding Angles
When two parallel lines are intersected by a transversal, the angles in matching corners are called corresponding angles. These angles are equal in measure.
#### Corresponding Angles Pairs from the Diagram
The pairs of corresponding angles in the given diagram are:
- Angle 1 and Angle 9
- Angle 2 and Angle 10
- Angle 3 and Angle 11
- Angle 4 and Angle 12
- Angle 5 and Angle 13
- Angle 6 and Angle 14
- Angle 7 and Angle 15
- Angle 8 and Angle 16
These pairs align vertically or horizontally in positions across the transversal where the parallel lines create congruent angles. The concept of corresponding angles is crucial in geometry for proving lines are parallel and solving for unknown angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bd06414-f1f6-4940-956f-9c39fe649804%2F60677d8e-5111-4667-8db5-230e7c1c24b8%2Fqgxptlp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Corresponding Angles in Parallel Lines
**Question 10:** Which pairs of angles are corresponding angles?
#### Diagram Description
The image provides a diagram featuring two sets of parallel lines intersected by a transversal. The angles at the intersection points are labeled from 1 to 16. The lines and angles are arranged as follows:
1. The first set of parallel lines and the transversal create angles 1 through 8.
2. The second set of parallel lines and the same transversal create angles 9 through 16.
#### Intersection Points
**First Intersection:**
- Top left of the diagram: Angles 1, 2, 3, and 4.
- Top right of the diagram: Angles 5, 6, 7, and 8.
**Second Intersection:**
- Bottom left of the diagram: Angles 9, 10, 11, and 12.
- Bottom right of the diagram: Angles 13, 14, 15, and 16.
#### Important Concepts - Corresponding Angles
When two parallel lines are intersected by a transversal, the angles in matching corners are called corresponding angles. These angles are equal in measure.
#### Corresponding Angles Pairs from the Diagram
The pairs of corresponding angles in the given diagram are:
- Angle 1 and Angle 9
- Angle 2 and Angle 10
- Angle 3 and Angle 11
- Angle 4 and Angle 12
- Angle 5 and Angle 13
- Angle 6 and Angle 14
- Angle 7 and Angle 15
- Angle 8 and Angle 16
These pairs align vertically or horizontally in positions across the transversal where the parallel lines create congruent angles. The concept of corresponding angles is crucial in geometry for proving lines are parallel and solving for unknown angles.
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