Chapter 4, Problem 16CUR

To determine

Prove $\overleftrightarrow{MO}$ is the perpendicular bisector of $\overline{NP}$ .

Explanation of Solution

Given:

  

  $\overline{MN}\cong \overline{MP}$

  $\angle NMO\cong \angle PMO$

Calculation:

Consider the $\Delta MNO\text{ and }\Delta \text{MPO}$ :

  $\overline{MN}\cong \overline{MP}$

  $\angle NMO\cong \angle PMO$

  $\overline{MO}\cong \overline{MO}$

So, by SAS Postulate, $\Delta MNO\cong \Delta \text{MPO}$ .

So, $\overline{NO}\cong \overline{PO}$ .

Hence , by Theorem 4-6 , $\overleftrightarrow{MO}$ is the perpendicular bisector of $\overline{NP}$ .

Hence proved.