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If a quadrilateral has one pair of opposite sides both congruent and parallel, then it is a parallelogram

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ABCD is a parallelogram

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If two lines cut by a transversal form congruent alternate interior angles, then they are parallel

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AB is parallel to CD

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Corresponding parts of congruent triangles are congruent (CPCTC)

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Angle OAB is congruent to angle OCD

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Corresponding parts of congruent triangles are congruent (CPCTC)

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AB is congruent to CD

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Given

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Triangle AOB is congruent to Triangle COD