Question

Write a proof to show that opposite sides of a parallelogram are congruent. Be sure to...

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.

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Answer #1

Given

Parallelogram .

What To Show

and .

Proof

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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