Lines and Angle Relationships Section 3.5 Proving Lines Parallel Lines and Angle Relationships

Converse of a Statement Inter-change the words following the “if” with the words following the “then” in a sentence. Example: If it rains then the grass grows. Converse: If the grass grows then it rains.

Parallel Postulate: If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

Corresponding s Postulate If two lines are parallel, then corresponding <‘s are congruent. 1 2 l m

Corresponding s Converse If 2 lines are cut by a transversal so that corresponding s are , then the lines are . ** If 1  2, then l m. 1 2 l m

Alt. Int. s If 2 lines are parallel, then alternate interior angles are congruent. 1 2 l m

Alt. Int. s Converse If 2 lines are cut by a transversal so that alt. int. s are , then the lines are . ** If 1  2, then l m. 1 2 l m

Consecutive Int. s If 2 lines are parallel, then consecutive interior angles are supplementary (180°). l m 1 2

Consecutive Int. s Converse If 2 lines are cut by a transversal so that consecutive int. s are supplementary, then the lines are . ** If 1 & 2 are supplementary, then l m. l m 1 2

Alt. Ext. s If 2 lines parallel, then alternate exterior angles are congruent. l m 1 2

Alt. Ext. s Converse If 2 lines are cut by a transversal so that alt. ext. s are , then the lines are . ** If 1  2, then l m. l m 1 2

Ex: Based on the info in the diagram, is p q ? If so, give a reason. Yes, alt. ext. s conv. No p q p q p q

Ex: Find the value of x that makes j  k . The angles marked are consecutive interior s. Therefore, they are supplementary. x + 3x = 180 4x = 180 x = 45 xo 3xo j k

Are there any parallel lines In this bookcase? How do you know?

Assignment: Textbook p. 211, #’s 8 – 21 all