Question

State whether True or False: Each point on a perpendicular bisector is such that it forms an isosceles triangle with the given line segment.

• A. True
• B. False

Answer 1

The correct option is A

True

Consider the figure above. Here, XY is the perpendicular bisector of a line AB. Let P be any random point on XY.
AM = BM (Perpendicular bisector divides a line segment into two equal halves)
$\angle$ PMA = ​$\angle$ PMB = 90${}^{\circ }$
Also PM is common.
So $△$ PMA $\cong$ $△$ PMB (RHS Rule)
$\therefore$ PA = PB (CPCT)
Hence, $△$ PAB is an isosceles triangle.
So, the given statement is true.