In the given figure, T is a point on side QR of triangle PQR and S is a point such that RT=ST.Prove that PQ + PR > QS
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In triangle PQR, we have,
PQ + PR > QR [In a triangle, sum of any two sides is always greater than third side.]
PQ + PR > QT + TR [AS, QR = QT + TR]
PQ + PR > QT + TS [ as, TR = TS ] ..................................(1)
In triangle QST, we have,
QT + TS > QS [In a triangle, sum of any two sides is always greater than third side.] ...........(2)
From (1) and (2), we can conclude that,
PQ + PR > QS
PQ + PR > QR [In a triangle, sum of any two sides is always greater than third side.]
PQ + PR > QT + TR [AS, QR = QT + TR]
PQ + PR > QT + TS [ as, TR = TS ] ..................................(1)
In triangle QST, we have,
QT + TS > QS [In a triangle, sum of any two sides is always greater than third side.] ...........(2)
From (1) and (2), we can conclude that,
PQ + PR > QS
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