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Prove that the opposite angles of a parallelogram are congruent.
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Well, that's a property of parallelograms.
But if you must prove it, I say you draw a diagonal from one angle to the opposite one, and then prove that the two triangles formed are congruent, since their three sides have the same length.
After that, just prove that the opposite angles are congruent because correspondent angles on congruent triangles are congruent.. @BIGDOG96
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