a point s is in the interior of triangle PQR prove that PQ+PR>SQ+ SR
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Produce QS to intersect PR at t.
From ΔPQT we have,
PQ+PT>QT [sum of 2 sides of a Δ is greater than the 3rd]
i.e. PQ+PT>SQ+ST (1)
From ΔTSR we have ,
ST+TR>SR (2)
By adding (1)&(2),
PQ+QT+ST+TR>SQ+ST+SR
∴PQ+PT+TR>SQ+SR
∴PQ+PR>SQ+SR
From ΔPQT we have,
PQ+PT>QT [sum of 2 sides of a Δ is greater than the 3rd]
i.e. PQ+PT>SQ+ST (1)
From ΔTSR we have ,
ST+TR>SR (2)
By adding (1)&(2),
PQ+QT+ST+TR>SQ+ST+SR
∴PQ+PT+TR>SQ+SR
∴PQ+PR>SQ+SR
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