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SECTION 1-5

SECTION 1-5. Exploring Angle Pairs. OBJECTIVE. To identify special angle pairs and use their relationships to find angle measures. VOCABULARY. Adjacent Angles – two coplanar angles with a common side, a common vertex, and no common interior points. 1 and 2 3 and 4. 3. 4. 1. 2.

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SECTION 1-5

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  1. SECTION 1-5 Exploring Angle Pairs

  2. OBJECTIVE To identify special angle pairs and use their relationships to find angle measures

  3. VOCABULARY Adjacent Angles – two coplanar angles with a common side, a common vertex, and no common interior points. 1 and 2 3 and 4 3 4 1 2

  4. VOCABULARY Vertical angles – two angles whose sides are opposite rays (formed by the intersection of two lines). 3 1 and 2 3 and 4 1 2 4

  5. VOCABULARY Complementary angles – two angles whose measures have a sum of 90˚. Each angle is called the complement of the other. 43˚ 1 and 2 A and B A 1 47˚ 2 B

  6. VOCABULARY Supplementary angles – two angles whose measures have a sum of 180˚. Each angle is called the supplement of the other. 160˚ 20˚ B 1 and 2 A and B A 1 2

  7. CLASS WORK Use the diagram at the right. Is each statement true? Explain. 1. 2 and 5 are adjacent angles. 2. 1 and 4 are vertical angles. 3. 4 and 5 are complementary.

  8. CLASS WORK Name an angle or angles in the diagram described by each of the following. 4. complementary to BOC 5. supplementary to DOB 6. adjacent and supplementary to AOC

  9. VOCABULARY Linear pair – pair of adjacent angles whose non-common sides are opposite rays. The angles of a linear pair form a straight angle. D ABD and DBC A B C

  10. KEY CONCEPT D A B C

  11. VOCABULARY Angle bisector – ray that divides an angle into two congruent angles. OB is the angle bisector of AOC B A C O

  12. CLASS WORK 7. Algebra In the diagram, XY bisects WXZ. a. Solve for x and find mWXY. b. Find mYXZ. c. Find mWXZ.

  13. COMPARE AND CONTRAST Relationships you can assume true without marks: Relationships that must be marked: • Angles are adjacent. • Angles are adjacent supplementary (form a line). • Angles are vertical angles. • Angles or segments are congruent. • An angle is a right angle. • Angles are complementary.

  14. Summary Angles pairs with special totals: Complementary angles sum to be 90°. Supplementary angles sum to be 180°. Angle pairs formed by intersecting lines. Adjacent angles are a linear pair that sum to be 180 °. Opposite angles are vertical angles that are congruent.

  15. EXIT PROBLEM In the diagram at the right, mHKI =48. Find each of the following. mHKJ mIKJ mFKG mFKJ

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