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. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
True
B
False

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

is equidistant from points

and

We have to prove that

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

bisector of

.
Hence, the given statement is true.

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.

Solution:

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