Section 3-4 Parallel and Perpendicular lines. Michael Schuetz

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

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

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

t m n Proof of Theorem 3-9: Given: In a plane, Prove: m//n 1 2 Statements Reasons 1. Given 2. Definition of perpendicular 3. Definition of congruence 4. Converse of Corresponding Angles.

Proving a Relationship Between Two Lines c d b a Given: In a plane, Prove: Statements Reasons 1. Given 2. If two lines are perpendicular to the same line, then they are parallel to each other. 3. If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

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