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Sect. 3.2 Proof and Perpendicular Lines. Goal 1 Comparing Types of Proofs Goal 2 Proving Results about Perpendicular Lines Comparing Types of Proofs F a) Name a line that appears to be parallel to EH be parallel to D C HC c) Name a line that appears to be skew to H G b) Name a line that appears to E A B BC d) Name a plane that appears to be parallel to plane GDA. Comparing Types of Proofs Theorem 3.1 If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. g gh h Comparing Types of Proofs Theorem 3.2 If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 2 1 1 and 2 are complementary. Comparing Types of Proofs Theorem 3.3 If two lines are perpendicular, then they intersect to form four right angles. Proving Results About Perpendicular Lines A Example 2 Given: AB BC Prove: 1 and 2 are complementary Statements 2 1 B Reasons 1. AB BC 1. Given 2. ABC is a right angle 2. def. of perpendicular lines 3. m ABC = 90° 3. def. of right angle 4. m1 + m2 = m ABC 4. Angle Addition Postulate 5. m1 + m2 = 90° 5. Substitution 6. 1 and 2 are complements 6. def. of complementary angles C Given: 1 is a right angle Prove: 3 is a right angle 1 3 Given: 1 is a right angle Prove: 3 is a right angle 1 3 1 3 a. 1 is a right b. m1 = m3 m1 = 90° d. c. m 3 = 90° e. 3 is a right f. Homework 3.2 11-16, 18, 26, 27, 29-36