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.
Prove that ∠F \(\mathsf{ \cong }\) ∠H.
Create your proof by placing the following steps in the correct order.
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Draw diagonal EG to create
△EFG and △EHG.
By SSS, △EFG \(\mathsf{ \cong
}\) △EHG.
In parallelogram EFGH, prove
∠F \(\mathsf{ \cong }\) ∠H.
By the definition of a
parallelogram, EF
\(\mathsf{ \cong }\) HG
and FG \(\mathsf{ \cong
}\) EH. Also, FH
\(\mathsf{ \cong }\) FH by
the Reflexive Property of
Congruence.
By CPCTC, ∠F \(\mathsf{
\cong }\) ∠H.
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You just proved that opposite angles in a parallelogram are congruent.
