Question

Converse of Perpendicular bisector theorem?
Converse of the Perpendicular Bisector Therom: any point equidistant from the endpoints of the segment lies on the perpendicular bisector of the segment. (we are trying to prove this)

Given AD=BD
AE=BE
Prove DE is the perpendicular bisector of AB.

The picture shows segment AB with line DE intersecting it at point C.

The table has some statements filled in:
1) AD=BD, AE=BE (given)
2) DE=DE
3)
4)
5)
6)
7)
8) linear pair
9)
10)
11)
12) right angles
13)
14)C is the midpoint of AB
15) DE bisector.

Thanks