Chapter 4.7, Problem 18WE

To determine

To prove: $\overleftrightarrow{SV}$ is perpendicular bisector of $\overline{ED}$ .

Answer to Problem 18WE

Explanation of Solution

Given information:

Given figure,

Given,

$S$ is equidistant from $E$ and $D$ ;

$V$ is equidistant from $E$ and $D$ .

Calculation:

$S$ is equidistant from $E$ and $D$ , therefore $S$ lies on the perpendicular bisector of $\overline{ED}$ .

Also $V$ is equidistant from $E$ and $D$ , therefore, point $V$ lies on the perpendicular bisector of $\overline{ED}$ .

Further points $S$ and $V$ both lie on the perpendicular bisector of $\overline{ED}$ , so the line joining points $S$ and $V$ matches with the perpendicular bisector of $\overline{ED}$ , or one can say that $\overleftrightarrow{SV}$ itself is the perpendicular bisector of $\overline{ED}$ .