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.


Answer :

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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