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Transcript
2.5 Proving Angles Congruent Vocabulary Terms vertical angles—angles who's sides are opposite rays 1and 2 1 3 4 3and4 2 Theorem 2.1—Vertical Angles Thm vertical angles are congruent 1 2 3 4 Vocabulary Terms adjacent angles—angles who have a common side and a common vertex **share a side 1 2 3 4 Vocabulary Terms complementary angles— two angles who add up to 90º A is a compliment to B 1 2 50 A 40 B supplementary angles—two angles who add up to 180º **make a straight line Ex 1: Identify each type of angle a) Complementary 2,3 2 1 b) Vertical 5 3,5 c) Supplementary 4,5 4,3 3 4 Ex 2: What can you conclude from the diagram? 3 4 5 1 2 1 2 Can I say… 3, 4 are adjacent 3 4 No 4, 5 are supplementary 2 5 180 2, 4 Yes are vertical Theorems Theorem 2-2: Supplementary Thm If 2 angles are supplements of the same angle (or congruent angles), then the 2 angles are congruent 1 1 2 3 2 3 **same for compliments Theorems Theorem 2-4: Right Angles All right angles are congruent Theorem 2-5: If 2 angles are congruent and supplementary, then each is a right angle Ex 3: Solve for variables a) 2 y 3y 6 y 6 y6 4x 2y 3y - 6 4 x 2 6 180 4 x 12 180 4 x 168 x 42 Ex 3: Solve for variables b) y 2x + 3 4x - 101 4 x 101 2 x 3 2 x 104 x 52 2 52 3 y 180 104 3 y 180 107 y 180 y 73 HW 2-5: WS 2-5