Chapter 5.1, Problem 39PPS

To determine

To prove: The relation $EA=EB$ .

Explanation of Solution

Given information:

The given triangle shown in figure (1).

  

Figure (1)

Th given relations are.

  $\overline{DE}$ is a perpendicular bisector of $\overline{AB}$ .

Proof:

Definition of bisector $E$ is a midpoint of $\overline{AB}$ .

One has $\overline{AE}\cong \overline{BE}$ by using midpoint theorem.

  $\angle EDA$ and $\angle EDB$ are right angles. So, one has $\angle EDA\cong \angle EDB$ , because right angles are congruent.

Using reflexive property of congruence.

  $\overline{ED}\cong \overline{ED}$

Using SAS congruence postulate.

  $\begin{array}{l}\overline{EA}\cong \overline{EB}\\ EA=EB\end{array}$

From the above, $EA=EB$ .

Hence, proved.