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Question

In the below-shown figure if AP=BP, AQ=BQ, then can we say that AM=BM?


A

True

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B

False

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Solution

The correct option is A

True


In the given figure,
PA=PB (Given)
AQ=BQ (Given)
PQ is common.
So, Δ PAQ Δ PBQ (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.


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