Q. 43.8( 23 Votes )

In figure 5.41, seg PD is a median of ΔPQR, Point T is the midpoint of seg PD. Produced QT intersects PR at M. Show that

[Hint : draw DN || QM.]


Answer :

PD is median so QD = DR (median divides the side opposite to vertex into equal halves)

T is mid-point of PD


PT = TD


In ΔPDN


T is mid-point and is to TM (by construction)


TM is mid-point of PN


PM =MN……………….1


Similarly in ΔQMR


QM DN (construction)


D is mid –point of QR


MN = NR…………………..2


From 1 and 2


PM = MN = NR


Or PM = 1/3 PR


hence proved




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