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Geometry B Date: _____________ 3.3 Proving Lines Parallel Objective: To use the angles formed by a transversal to prove two lines are parallel Recall: Conditional: ____________________________________________________________ Converse: ______________________________________________________________ Last time, we said “If two lines are parallel, then the corresponding angles are equal.” The converse states: _____________________________________________________________ Ex. 1: Converse of the Corresponding Angles Postulate Tell whether the two lines are parallel based on the given information. If they are, explain why and write a statement to show that they are parallel. a. 4 8 b. 1 5 c. m3 4x 80 , m7 3x 50 , x 30 d. m2 4x 25 , m6 5x 12 , x 13 The other angle pair theorems have converses that are true as well. Write the converse of each statement (Remember: Converse means flip) Alternate Interior Angles: If two lines are parallel, then the alternative interior angles are congruent. Converse: ___________________________________________________________________________ Alternate Exterior Angles: If two lines are parallel, then the alternate exterior angles are congruent. Converse: ___________________________________________________________________________ Consecutive Interior Angles: If two lines are parallel, then the consecutive interior angles are supplementary. Converse: __________________________________________________________________________ Ex. 2: Using the Converse of the Other Angle Postulates Tell whether the two lines are parallel based on the given information. If they are, explain why and write a statement to show that they are parallel. a. 4 8 b. 7 3 c. m2 10x 8 , m3 25x 3 , x 5 d. m1 2x , mx 50 , x 50 HW: 3.3 Worksheet