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Show that opposite angles in a parallelogram are congruent.

Thus far in Evan's story, Detective Reese has proven that opposite angles in a parallelogram are congruent. Use the steps demonstrated by Reese to create your own proof.

parallelogram

Prove that ∠F ∠H.

Create your proof by placing the following steps in the correct order.

Draw diagonal EG to create △EFG and △EHG.

By SSS, △EFG  △EHG.

In parallelogram EFGH, prove ∠F ∠H.

By the definition of a parallelogram, EF HG and FG EH. Also, FH FH by the Reflexive Property of Congruence.

By CPCTC, ∠F ∠H.
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You just proved that opposite angles in a parallelogram are congruent.