Question

In triangle PQR, PS and RT are mediana and SM parallel RT. Prove that QM=1/4(PQ)

Answer 1

it is given that RT is the median of triangle PQR. So, TQ=TP
Now, in triangle QRT
S is the mid point of QR( it is given that PS is the median so QS =RS )
And SM is parallel to TR (also given)
so by converse of mid point theorem
M is the mid point of TQ
hence , QM=1/2TQ
SO,QM= 1/2 *1/2(PQ). (SINCE TQ=1/2PQ)
so, QM=1/4(PQ)
HENCE PROVED

Answer 2

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