Section 3-4 Parallel and Perpendicular lines. Michael Schuetz

Theorem 3-8: Two Parallel Lines Theorem. Theorem If Then If two lines are parallel to the same line, then they are parallel to each other. a b c

Theorem 3-9: Two Perpendicular Lines Theorem. Theorem If Then In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. t m n

Theorem 3-10: Perpendicular Transversal Theorem. Theorem If Then In a plane if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other. n l m

Proof of Theorem 3-9:  Given: In a plane,  Prove: m//n StatementsReasons 1. Given 2. Definition of perpendicular 3. Definition of congruence 4. Theorem 3-4: If corresponding angles are congruent then the lines are parallel. t m n 1 2

 Given: In a plane,  Prove: Proving a Relationship Between Two Lines StatementsReasons 1. Given 2. Theorem 3-9: Two Perpendiculars Theorem. If two lines are perpendicular to the same line, then they are parallel to each other. 3. Theorem 3-10: Perpendicular Transversal Theorem. If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. c d ba

Homework:  P. 167, #’s 8, 10-15, 19-24, 27-32