State whether the given statement is true or false.AB is a line segment. C and D are points on opposite sides of AB such that each of them is equidistant from the point A and B as in the figure. The line CD is the perpendicular bisector of AB.

# State whether the given statement is true or false.AB is a line segment. C and D are points on opposite sides of AB such that each of them is equidistant from the point A and B as in the figure. The line CD is the perpendicular bisector of AB.

1. A
True
2. B
False

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### Solution:

The given statement is true.
Concept- We solve this problem by applying the ⁷concept of congruent triangles to obtain the necessary condition, i.e., to prove the perpendicular bisector.
Here, is equidistant from points and .
and is equidistant from points and We have to prove that and In and (1)
common)
..... (SSS congruence rule)
Hence, ....... (C.P.C.T) ….(3)
In (SAS congruence rule)
C.P.C.T)
(C.P.C.T)
As is a line segment,
Hence, and is bisector of .
​Hence, the given statement is true.

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