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Home > CCG > Chapter Ch7 > Lesson 7.3.1 > Problem 7-124

7-124.

Carolina compared her proof to Penn’s work in problem 7-113. Like him, she wanted to prove that if and , then . 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 .  

 Statements 

Reasons

  1. and  

  • Given

  1.  

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

  1.  

  • Substitution

  1.  

  • If lines are parallel, corresponding angles are equal.

  1.  

  • Vertical angles are equal.

  1.  

  • Substitution

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.

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