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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 justification for each statement.  

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.

  1.  

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

  1.  

  1.  

  1.  

  1.  

Two increasing lines, B F, & C G, cross two horizontal lines, A D, & E H, angles are labeled at intersections as follows: top left intersection, right bottom angle, a, bottom left intersection, left top angle, b, bottom right intersection, left top angle, c, right bottom angle, d.