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Home > GC > Chapter 7 > Lesson 7.2.6 > Problem 7-96

7-96.

Penn started the proof below to show that if and , then . Unfortunately, he did not provide reasons for his proof. Copy his proof and provide a justification for each statement.

Two increasing transversal lines, BF, and CG, cross two possibly horizontal lines, AD, and EH. At the intersection of lines, AD and BF: interior bottom angle is a. At the intersection of lines, EH and BF: exterior top angle is b. At the intersection of lines, EH and CG: interior top angle is c, exterior bottom angle is d.

For each numbered statement, write how you know it to be true. Think about how angles and parallel lines relate to each other.

 Statements 

Reasons

  1. and

Given information.

When lines are parallel, then the alternate interior angles are congruent.