In triangle PQR, PS and RT are medians and SM is parallel to RT. Prove that QM= 1/4 PQ.

Given : A ΔPQR in which PS and RT are the medians and SM || RT.

To prove :

Proof : PS and RT are the medians in ΔPQR.

∴ S is mid point of QR and. T is mid point of PQ.

∴ QS = SR and PT = TQ    ..(1)

In ΔQTR, S is mid point of QR and SM || RT.

∴ By mid point theorem, M is mid point of QT.

⇒ QM = MT

         

Thus,

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