+292 Given: parallelogram EFGH
Prove: EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ .
+2446 | 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 |
+2446 | 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 |
