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Name the relationship: complementary. 8) 7) 9. b a

Name the relationship: complementary. 8) 7) 9. b a

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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**Complementary and Linear Pair Relationships in Angles** **Complementary Angles:** **7) Diagram Explanation:** - Two angles, labeled `a` and `b`, are formed by two intersecting lines. - Angle `a` is adjacent to angle `b`, sharing a common arm. - The diagram includes a right angle (90 degrees) symbol between the two angles, indicating that the sum of angles `a` and `b` is 90 degrees. This defines them as complementary angles. **8) Diagram Explanation:** - Similar to the previous diagram, two angles, `a` and `b`, are adjacent. - There is a right angle symbol where the two arms meet, indicating that angles `a` and `b` add up to 90 degrees, representing a complementary relationship. **Linear Pair of Angles:** **9) Diagram Explanation:** - Two angles, labeled `a` and `b`, are shown on a straight line. - These angles are adjacent and together form a straight line, thus summing up to 180 degrees. This is a defining characteristic of a linear pair of angles. **10) Diagram Explanation:** - Angles `a` and `b` are adjacent and form a triangle shape within the diagram. - The straight line on one side further emphasizes that the combination of these two angles results in a linear pair, summing to 180 degrees. These diagrams illustrate fundamental concepts in geometry related to complementary angles, which sum to 90 degrees, and linear pairs, which sum to 180 degrees, helping in understanding angle relationships in various geometric contexts.
Transcribed Image Text:**Complementary and Linear Pair Relationships in Angles** **Complementary Angles:** **7) Diagram Explanation:** - Two angles, labeled `a` and `b`, are formed by two intersecting lines. - Angle `a` is adjacent to angle `b`, sharing a common arm. - The diagram includes a right angle (90 degrees) symbol between the two angles, indicating that the sum of angles `a` and `b` is 90 degrees. This defines them as complementary angles. **8) Diagram Explanation:** - Similar to the previous diagram, two angles, `a` and `b`, are adjacent. - There is a right angle symbol where the two arms meet, indicating that angles `a` and `b` add up to 90 degrees, representing a complementary relationship. **Linear Pair of Angles:** **9) Diagram Explanation:** - Two angles, labeled `a` and `b`, are shown on a straight line. - These angles are adjacent and together form a straight line, thus summing up to 180 degrees. This is a defining characteristic of a linear pair of angles. **10) Diagram Explanation:** - Angles `a` and `b` are adjacent and form a triangle shape within the diagram. - The straight line on one side further emphasizes that the combination of these two angles results in a linear pair, summing to 180 degrees. These diagrams illustrate fundamental concepts in geometry related to complementary angles, which sum to 90 degrees, and linear pairs, which sum to 180 degrees, helping in understanding angle relationships in various geometric contexts.
**Name the Relationship: Adjacent** **Diagram 11:** - Two angles labeled \(a\) and \(b\) share a common arm. They are positioned such that the vertex of both angles is the same point, demonstrating that they are adjacent angles. **Diagram 12:** - Two angles labeled \(a\) and \(b\) share a common vertex and a common side, lying in the same plane, portraying adjacent angles once more. **Name the Relationship: Vertical** **Diagram 13:** - Two intersecting lines form two angles labeled \(a\) and \(b\). These angles are opposite each other at the intersection, indicating that they are vertical angles. **Diagram 14:** - Similar to Diagram 13, two intersecting lines create two angles labeled \(a\) and \(b\) directly opposite each other, illustrating vertical angles.
Transcribed Image Text:**Name the Relationship: Adjacent** **Diagram 11:** - Two angles labeled \(a\) and \(b\) share a common arm. They are positioned such that the vertex of both angles is the same point, demonstrating that they are adjacent angles. **Diagram 12:** - Two angles labeled \(a\) and \(b\) share a common vertex and a common side, lying in the same plane, portraying adjacent angles once more. **Name the Relationship: Vertical** **Diagram 13:** - Two intersecting lines form two angles labeled \(a\) and \(b\). These angles are opposite each other at the intersection, indicating that they are vertical angles. **Diagram 14:** - Similar to Diagram 13, two intersecting lines create two angles labeled \(a\) and \(b\) directly opposite each other, illustrating vertical angles.
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