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7-60.

What else can you prove about quadrilaterals? Prove that if a pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral must be a parallelogram. For example, for the quadrilateral at right, given that and , show that . Organize your reasoning in a proof (two-column or flowchart). Then record your theorem in your Theorem Graphic Organizer.

Quadrilateral A, B, C, D. Side A, B and side C, D are both marked with two tick marks and one arrow each.

If a pair of opposite sides is parallel and congruent then the quadrilateral is a parallelogram.
Use the if part of the statement as the givens, and the then part of the statement as the prove portion in the proof.

Statements

Reasons

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Given

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Given

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Segment is congruent to itself

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Alt. int. angles parallel   

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 is a
parallelogram