Question

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

Answer 1

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