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Which angles are corresponding angles? 14 9 10 11 12 14 13 16 15 O 28 and 23 O 23 and 211 O 27 and 23 O none of these

Which angles are corresponding angles? 14 9 10 11 12 14 13 16 15 O 28 and 23 O 23 and 211 O 27 and 23 O none of these

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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### Identifying Corresponding Angles In the image, we are asked to identify which angles are corresponding angles given the diagram of two parallel lines intersected by two transversals. ### Diagram Description The diagram consists of two sets of parallel lines labeled \(a\) and \(b\). These parallel lines are intersected by two transversals labeled \(c\) and \(d\). The intersections form several angles as follows: - On line \(a\) and transversal \(c\): - \( \angle 1 \), \( \angle 2 \) at the top left intersection. - \( \angle 3 \), \( \angle 4 \) at the top right intersection. - \( \angle 5 \), \( \angle 6 \), \( \angle 7 \), \( \angle 8 \) on each section formed by the intersection with \(a\). - On line \(b\) and transversal \(c\): - \( \angle 9 \), \( \angle 10 \) at the bottom left intersection. - \( \angle 11 \), \( \angle 12 \) at the bottom right intersection. - \( \angle 13 \), \( \angle 14 \), \( \angle 15 \), \( \angle 16 \) on each section formed by the intersection with \(b\). ### Question and Answer Options **Question:** Which angles are corresponding angles? **Answer Options:** - \( \bigcirc \) \( \angle 8 \text{ and } \angle 3 \) - \( \bigcirc \) \( \angle 3 \text{ and } \angle 11 \) - \( \bigcirc \) \( \angle 7 \text{ and } \angle 3 \) - \( \bigcirc \) none of these ### Explanation of Corresponding Angles Corresponding angles are angles that are in the same relative position at each intersection where a straight line crosses two other parallel lines. In this context: - \( \angle 8 \text{ and } \angle 3 \) are corresponding angles because they occupy the same relative position at the intersections of the transversals with the parallel lines. Therefore, the correct answer is: - \( \bigcirc \) \( \angle 8 \text{ and } \angle 3 \).
Transcribed Image Text:### Identifying Corresponding Angles In the image, we are asked to identify which angles are corresponding angles given the diagram of two parallel lines intersected by two transversals. ### Diagram Description The diagram consists of two sets of parallel lines labeled \(a\) and \(b\). These parallel lines are intersected by two transversals labeled \(c\) and \(d\). The intersections form several angles as follows: - On line \(a\) and transversal \(c\): - \( \angle 1 \), \( \angle 2 \) at the top left intersection. - \( \angle 3 \), \( \angle 4 \) at the top right intersection. - \( \angle 5 \), \( \angle 6 \), \( \angle 7 \), \( \angle 8 \) on each section formed by the intersection with \(a\). - On line \(b\) and transversal \(c\): - \( \angle 9 \), \( \angle 10 \) at the bottom left intersection. - \( \angle 11 \), \( \angle 12 \) at the bottom right intersection. - \( \angle 13 \), \( \angle 14 \), \( \angle 15 \), \( \angle 16 \) on each section formed by the intersection with \(b\). ### Question and Answer Options **Question:** Which angles are corresponding angles? **Answer Options:** - \( \bigcirc \) \( \angle 8 \text{ and } \angle 3 \) - \( \bigcirc \) \( \angle 3 \text{ and } \angle 11 \) - \( \bigcirc \) \( \angle 7 \text{ and } \angle 3 \) - \( \bigcirc \) none of these ### Explanation of Corresponding Angles Corresponding angles are angles that are in the same relative position at each intersection where a straight line crosses two other parallel lines. In this context: - \( \angle 8 \text{ and } \angle 3 \) are corresponding angles because they occupy the same relative position at the intersections of the transversals with the parallel lines. Therefore, the correct answer is: - \( \bigcirc \) \( \angle 8 \text{ and } \angle 3 \).
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