Write a proof to show that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
What To Show
Draw diagonal .
Since is a transversal to parallel lines and , because they are alternate interior angles.
Now, segment is congruent to itself (reflexive proeprty) so, .
Since is parallel to , because they are alternate interior angles.
By ASA congruence, .
Since corresponding parts of congruent triangles are congruent, and .
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