1. Lesson 3.2 Proof and Perpendicular Lines

2. Theorem 3.1  If two lines intersect to form a linear pair of congruent angles, then the lines are  Ex 1 ABC D m<ABD = m<DBC and a linear pair, DB AC

3. Why????? StatementsReasons 1. <1 and <2 are a linear pair1. 2. 3. <1 and <2 are supplementary3. 4. m<1 + m<2 = 1804. 5. m<1 = m<25. 6. m<1 + m<1 = 1806. 7.2(m<1) = 1807. 8. m<1 = 908. 9. <1 is a right angle.9. 10. h g 1 2

4. Theorem 3.2  If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.  Ex. 2 H F G J <FGJ is complementary to <JGH

5. Given: m ⊥ n Prove: <1 and <2 are complementary StatementsReasons 1. m ⊥ n 1. 2. <mpn is a right angle2. 3. m<mpn = 903. 4. m<1 + m<2 = m<mpn4. 5. m<1 + m<2 = 905. 6. <1 and <2 are complementary 6. m n 1 2 p

6. Theorem 3.3  If 2 lines are perpendicular, then they intersect to form four right angles. m l

7. Why??? StatementsReasons 1. <1 and <2 are a linear pair1. 2. j ⊥ k 2. 3.3. Linear Pair Postulate 4. m<1 + m<2 = 1804. 5. <1 is a right angle5. 6.6. Defn. of right angles 7. 90 + m<2 = 1807. Given: j ⊥ k, <1 and <2 are a linear pair Prove: <2 is a right angle j k 1 2 8. m<2 = 908. 9. <2 is a right angle9.

8. Examples: Solve for x 1. 60° x ANSWER: 60 + x = 90 -60 -60 x = 30

9. Example 2 x 55° ANSWER: x + 55 = 90 -55 -55 x = 35

10. Example 3 27° (2x-9)° ANSWER: 2x – 9 + 27 = 90 2x +18 = 90 2x = 72 x = 36