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Question

In the below-shown figure if AP=BP and AQ=BQ, then AM should be equal to BM.

 



Correct Answer
A

True

Your Answer
B

False


Solution

The correct option is A

True


In the given figure,
PA=PB (Given)
AQ=BQ (Given)
PQ is common.
So, ΔPAQ ΔPBQ (SSS rule).
APQ=BPQ(CPCT).
Also, PA=PB (Given) and PM is common
Hence, PMA  PMB                 (SAS Rule)

So, AM=BM and PMA = PMB        (CPCT)

 PMA + PMB = 180            (Linear pair axiom),

PMA = PMB = 90

Therefore, PM, that is, PMQ is the perpendicular bisector of AB.

Hence AM=BM

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