Chapter 10.1, Problem 3PSA

To determine

To Prove: $\overline{OM}\text{ is an altitude}\text{.}$

Explanation of Solution

Given information :

We know that $\odot O,\overline{OM}\text{ is a median}$ of the $\Delta OAB$

  

Proof :

  $\begin{array}{l}\overline{OM}\text{ is a median}\text{.}\\ \text{then AM = MB (Given)}\\ OM=OM(\text{Reflexive property})\\ OA=OB(radius)\\ \Delta OAM\cong \Delta OBM(SSS\text{ Theorem})\\ \angle OMAand\angle OMB\text{ are right angles}\text{.}\\ \text{As equal angles that form a linear pair measure 90°}\text{.}\\ \text{OM}\perp AB,OMisaltitude.\end{array}$