In the following figure, PS and RT are medians of ∆ PQR and SM | | RT. Prove that

QM=1/4 PQ.

Given PS and RT are the medians of ∆ PQR, i.e. S and T are the mid-points of QR and PQ respectively,

Proof In ∆ QTR, S is the mid-point of QR and SM || RT So, by converse of mid-point theorem, M is mid-point of QT

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