Question

In rectangle PQRS and rectangle MNRL are rectangle. If point M is the midpoints of side PR prove that (i) SL = LR (ii) LN = 1/2 SQ

Answer 1

We have two rectangles -
PQRS and MNRL
In triangle PSR
Angle PSR = MLR = 90degree
Therefore ML // SP when SL is the transversal
M is the midpoint of PR (given)
By Mid point theorem we know a parallel line drawn from a mid point of a side of triangle meets at the Mid point of the opposite side.
Hence L is the mid-point of SR
(i) Therefore,
SL=LR (proved)
Similarly ,
If we construct a line from L which is parallel to SR
Then we would get point N which will be the mid point of QR (Mid point theorem)
Hence, When LN // SQ and L and N are mid points of SR and QR respectively,
(ii) LN = ½ SQ (By Mid point theorem) (Proved)