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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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.]

MHB - Math Part-II

In the adjacent figure 5.44, ABCD is a trapezium. AB || DC. Points M and N are midpoints of diagonal AC and DB respectively then prove that MN || AB.

MHB - Math Part-II

In figure 5.39, PQRS and MNRL are rectangles. If point M is the midpoint of side PR then prove that,

i. SL = LR. Ii. LN = 1/2SQ.

MHB - Math Part-II