Question

AB is a line -segment. P and Q are point on opposite sides of AB such that each of them is equidistant from the point AB. Show that line PQ is the perpendicular bisector of AB.​

Answer 1

Answer:

Since PA=QA=QB=QA

These four lines can be thought of as 4 equal sides of a quadrilateral .

Step-by-step explanation:

Now if 4 sides of a quadrilateral are equal it is a rhombus.

Also in a rhombus the diagonals bisect each other at 90°.

So PQ is perpendicular bisector of AB . And both PQ and AB are diagonals of our rhombus

APBQ.