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7-49.

Carolina compares her proof to Penn’s work in problem 7-39. Like him, she wants to prove that if and , then . Unfortunately, her statements are in a different order. Examine her proof below and help her decide if her statements are in a logical sequence to prove that .

Statements

Reasons

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Given

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If lines are parallel, alternate interior angles are equal.

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Substitution

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Given

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If lines are parallel, corresponding angles are equal.

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Vertical angles are equal.

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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.

Be sure to start with the "Given" statements. Then, if lines are parallel, which pairs of angles will be congruent?