S is any point on side QR of triangle PQR . show that PQ + QR + PR > 2PS
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S is any point on side QR of triangle PQR . show that PQ + QR + PR > 2PS
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S is any point on side QR of triangle PQR . show that PQ + QR + PR > 2PS.
In ∆PQS,
By using inequality of Triangles, The sum of any two sides of the ∆ is greater than the third side:
➛ PQ + QS > PS ----------(1)
And In ∆PRS,
Again by the same inequality,
➛ PR + SR > PS ----------(2)
Adding (1) and (2),
➛ PQ + QS + PR + SR > PS + PS
➛ PQ + (QS + SR) + PR > 2PS
➛ PQ + QR + PR > 2PS
Hence, Proved !!
Note that!!