In triangle PQR, PS and RT are medians and SM is parallel to RT Prove that QM= 1/4 PQ - Maths - Areas of Parallelograms and Triangles

Question

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

Harleen Birdi · Accepted Answer

Given : A Î”PQR in which PS and RT are the medians and SM || RT To prove : $QM = \frac{1}{4} PQ$ Proof : PS and RT are the medians in Î”PQR âˆ´ S is mid point of QR and T is mid point of PQ âˆ´ QS = SR and PT = TQ $= \frac{1}{2} PQ$ (1) In Î”QTR, S is mid point of QR and SM || RT âˆ´ By mid point theorem, M is mid point of QT â‡’ QM = MT $= \frac{1}{2} QT = \frac{1}{2} (\frac{1}{2} PQ) [Using (1)] = \frac{1}{4} PQ$ Thus, $QM = \frac{1}{4} PQ$

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