Given: parallelogram EFGH

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

Johnnyboy
Dec 11, 2017

#1**+1 **

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 |

TheXSquaredFactor
Dec 11, 2017

#1**+1 **

Best Answer

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 |

TheXSquaredFactor
Dec 11, 2017