In the below figure if AP=BP, AQ=BQ, then AM=BM?

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Question

In the below figure if AP=BP, AQ=BQ, then AM=BM?

Options:

A . True

B . False

C . Data insufficient

D . Cannot be determined

Answer: Option A
:
A

In the given figure,
AP = BP (Given)
AQ = BQ (Given)
PQ is common.
So, $Δ$ PAQ $≅$ $Δ$ PBQ (SSS rule).
$\Rightarrow ∠$ APQ= $∠$ BPQ (CPCT).
Also, AP = BP (Given) and PM is common
Hence, $△$ PMA $≅$ $△$ PMB (SAS Rule)

So, AM = BM

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