Question

In figure 5.41, seg PD is a median of triangle PQR.
Point T is the mid point of seg PD. Produced
PM
1
QT intersects PR at M. Show that
PR 3.
[Hint : draw DN || QM.]
​

Answer 1

PD is the median of QR.

So, D is the midpoint of QR.

DN is drawn parallel to QM.

By converse of midpoint theorem, N is the midpoint of MR. .....(1)

Similarly, T is the midpoint of PD

Also, DN || QM

So, By converse of midpoint theorem,

M is the midpoint of PN. .....(2)

From (1) and (2) we have

PM = MN = NR

⇒PMPR=PMPM+MN+NR=PMPM+PM+PM=13PM=13

⇒PMPR=13

Hence Proved.