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Home > CCG > Chapter 7 > Lesson 7.3.1 > Problem 7-124


Carolina compared her proof to Penn’s work in problem 7‑113. Like him, she wanted to prove that if AD EH and BF CG, then a = d. Unfortunately, her statements were in a different order. Examine her proof below and help her decide if her statements are in a logical order in order to prove that .



  1. and

  • Given

  • If lines are parallel, alternate interior angles are equal.

  • Substitution

  • If lines are parallel, corresponding angles are equal.

  • Vertical angles are equal.

  • Substitution

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.

Is it possible to know that in the 3rd statement? What step is out of order?