Q. 2

# 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.

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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