Parallel Lines and Transversals Section 3.3 and 3.4

Corresponding Angle Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 2 1

Alternate Interior Angle Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 1 2

Consecutive Interior or Same Side Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior (same side) angles are supplementary. 4 3

Alternate Exterior Angles Theorem If two lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 1 2

Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. if t s then p s s p t

Example What’s A’s relationship to the angle with the measure of 5x -3◦? Corresponding Angle Find the m A if x = 10◦. 47◦ What is the name of B and its measure? Consecutive Interior or Same Side Angle, 133◦ A B 5x -3◦

Example What is the relationship between A and B? Vertical Angles What is the relationship between A and C? Alternate Interior Angles What is the relationship between B and 65◦? Alternate Exterior Angles What is the m A, m B, and m C? m A = 65◦, m B = 65◦, m C = 65◦ A B 65◦ C

Corresponding Angle Postulate Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. 2 1

Alternate Interior Angle Theorem Converse If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 2 1

Consecutive Interior or Same Side Interior Angles Theorem Converse If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. 4 3

Alternate Exterior Angles Theorem Converse If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. 1 2

Example Find the value of x that makes lines d and f parallel. x = 6x - 25◦ -5x = -25◦ x = 5◦ 6x - 25◦ f x d

Example Find the value of x that would make line d and f parallel. 7x = 2x + 95◦ 5x = 95◦ x = 19◦ f 2x + 95◦ 7x d

Example Find the value of x that would make line d and f parallel. 3x = 2x + 137◦ x = 137◦ 2x + 137◦ f 3x d

Example Find the value of x that would make line d and f parallel. 4x + 2x - 60◦ = 180◦ 6x - 60◦ = 180◦ 6x = 240◦ x = 40◦ f 4x 2x - 60◦ d

Example Find the value of x that would make line d and f parallel. 4x + 3x - 30◦ = 180◦ 7x - 30◦ = 180◦ 7x = 210◦ x = 30◦ f 4x 3x - 30◦ d

What We Learned Today When parallel lines are cut by a transversal line, then: Corresponding Angles are Congruent Alternate Interior Angles are Congruent Alternate Exterior Angles are Congruent Consecutive Interior or Same Side Angles are supplementary We also learned about the converses of these statements.