CHAPTER 2: DEDUCTIVE REASONING

1. CHAPTER 2: DEDUCTIVE REASONING Section 2-5: Perpendicular Lines

2. PERPENDICULAR LINES Definition Perpendicular Lines: 2 lines that intersect to form right angles (90 degree angles). ┴is the symbol for perpendicular l┴mThis is read: “line l is perpendicular to line m” m l

3. EXAMPLE If m 1 = 90 , find the measure of each angle. m 2 = 90 m 3 = 90 m 4 = 90 2 1 3 4

4. THEOREMS Theorem 2-4: If lines are ┴, they form ≡ adjacent angles. Theorem 2-5: If 2 lines form ≡ adjacent angles, they are ┴. Theorem 2-6: If the non-common sides of 2 adjacent angles are ┴, then the angles are complementary.

5. OA ┴ OC m AOC = 90 m 1 + m 2 = m AOC m 1 + m 2 = 90 1 and 2 are complementary Given Def. of ┴ lines Angle Add. Post. Substitution Def. of complementary angles PROOF A B Given: OA ┴ OC Prove: 1 and 2 are complementary 1 C 2 O

6. m EYO m OYM m MYT m EYT 90 – 30 = 60 90 – 60 = 30 90 – 30 = 60 60 + 90 = 150 EXAMPLE If m GYE = 30, find each angle measure YE ┴ YM, YO ┴ GT O M E G T Y

7. EXAMPLE m EYO = 3x, m OYM = 2x + 15 Find x. 3x + 2x + 15 = 90 5x + 15 = 90 5x = 75 x = 15 O M E G T

8. EXAMPLE m GYE = x - 2, m EYO = 3x + 12 Find x. x – 2 + 3x + 12 = 90 4x + 10 = 90 4x = 80 x = 20 O M E G T

9. CLASSWORK/HOMEWORK • CLASSWORK Pg. 57: Classroom Exercises 1, 2-10 even • HOMEWORK Pg. 58: Written Exercises 2-24 even