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# Drag and drop a statement or reason to each box to complete the proof.

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Given: parallelogram EFGH

Prove: EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ .

Dec 11, 2017

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 parallelogram EFGH Given $$\overline{EF}\cong\overline{HG}$$ Property of a Parallelogram (If a quadrilateral is a parallelogram, then its opposite sides are congruent) $$\overline{EF}\parallel\overline{HG}$$ Definition of a Parallelogram (A quadrilateral that has opposite sides parallel is a parallelogram) $$\textcolor{red}{\angle FEG\cong\angle HGE\\ \angle EFH\cong\angle FHG}$$ Alternate Interior Angles Theorem $$\triangle EKF\cong\triangle GKH$$ ASA Congruence Postulate $$\textcolor{red}{\overline{EK}\cong\overline{KG}\\ \overline{FK}\cong\overline{KH}}$$ CPCTC
Dec 11, 2017
edited by TheXSquaredFactor  Dec 11, 2017

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 parallelogram EFGH Given $$\overline{EF}\cong\overline{HG}$$ Property of a Parallelogram (If a quadrilateral is a parallelogram, then its opposite sides are congruent) $$\overline{EF}\parallel\overline{HG}$$ Definition of a Parallelogram (A quadrilateral that has opposite sides parallel is a parallelogram) $$\textcolor{red}{\angle FEG\cong\angle HGE\\ \angle EFH\cong\angle FHG}$$ Alternate Interior Angles Theorem $$\triangle EKF\cong\triangle GKH$$ ASA Congruence Postulate $$\textcolor{red}{\overline{EK}\cong\overline{KG}\\ \overline{FK}\cong\overline{KH}}$$ CPCTC