Q2 of 35 Page 73

In figure 5.39,

The two rectangle PQRS and MNRL

In Δ PSR,


∠ PSR = ∠ MLR = 90°


∴ ML ∥ SP when SL is the transversal


M is the midpoint of PR (given)


By mid-point theorem a parallel line drawn from a mid-point of a side of a Δ meets at the Mid-point of the opposite side.


Hence L is the mid-point of SR


⇒ SL= LR


Similarly if we construct a line from L which is parallel to SR


This gives N is the midpoint of QR


Hence LN∥ SQ and L and N are mis points of SR and QR respectively


And LN = 1/2 SQ (mid-point theorem)




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In figure 5.38, points X, Y, Z are the midpoints of side AB, side BC and side AC of ΔABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.

3

In figure 5.40, ΔABC is an equilateral triangle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that ΔEFD is an equilateral triangle.

 4

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.]