Question 31170
Let lines AB and CD be parallel lines.
Let transversal EF cross AB and CD. 
Let angle 1 and angle 2 be corresponding angles formed by EF crossing lines AB and CD.
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Statement:  Angle 1 is congruent to angle 2. 
Reason: Theorem, if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
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Statement: 1/2 angle 1  = 1/2 angle 2 (They are congruent).
Reason: Definition of Bisector.
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Statement: The bisectors of angles 1 and angle 2 are parallel.
Reason. Theorem, if 2 lines cut be a tranversal form a pair of corresponding angles with the transversal, then the lines are parallel.
Cleomenius.