Question

Given: $S$is equidistant from $E$and $D$;$V$is equidistant from $E$and $D$.

Prove: $\overleftrightarrow{sv}$is the perpendicular bisector of $\overline{ET}$.

Short answer

It is being given that $S$is equidistant from $E$and $D$.

Therefore, $S$is lying on the perpendicular bisector of $ED$.

It is also being given that role="math" localid="1649238135856" $V$is equidistant from $E$and $D$.

Therefore, $V$is lying on the perpendicular bisector of $ED$.

As, $S$and $V$are lying on the perpendicular bisector of $ED$.

Therefore, the line joins the points $S$and $V$is congruent with the perpendicular bisector of $ED$.

Therefore, role="math" localid="1649238230824" $SV$is the perpendicular bisector of $ED$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the theorem 4-6.

Theorem 4-6 states that if a point is equidistant from the endpoints of a segment then the point lies on the perpendicular bisector of the segment.

Step 3. Write the proof for the statement that SV↔ is the perpendicular bisector of ED¯.

It is being given that $S$is equidistant from $E$and D.

Therefore, $S$is lying on the perpendicular bisector of $ED$.

It is also being given that $V$is equidistant from $E$and $D$.

Therefore, $V$is lying on the perpendicular bisector of $ED$.

As, $S$and $V$are lying on the perpendicular bisector of $ED$.

Therefore, the line joins the points $S$and $V$is congruent with the perpendicular bisector of $ED$.

Therefore, $SV$is the perpendicular bisector of $ED$.