Let PQRS be a convex quadrilateral as shown in the figure. QS is joined
We know that
In a triangle, the sum of two sides is always greater than the third side
Therefore,
In ΔPQS
PQ + QS > PS (1)
Again in ΔQRS
QR + RS > QS (2)
Adding both the inequalities
PQ + QS + QR + RS > PS + QR
or, PQ + QR + RS > PS (Hence Proved)
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