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SAS Criteria for Congruency

If P is any p...

Question

If P is any point in the interior of a triangle ABC, then PA + PB > AB + AC.

AB = AD

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AB = DC

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Solution

The correct option is B
AB = DC

[PB extended meets AC at M]

In $Δ B C M$ ,

BC + CM > BM ..... (1)

In $Δ A P M$ ,

AM + PM > AP ..... (2)

Adding (1) and (2), we get

BC + CM + AM + PM > BM + AP

BC + (CM + AM) > BM - PM + AP

BC + AC > BP + AP

So, the statement given is false.

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