Question

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=1/2 SQ.

Answer 1

SOLUTION:-

GIVEN BY:- 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
●here ,
(i) 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,

here,
●(ii) LN = ½ SQ (By Mid point theorem) (Proved)


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Answer 2

Answer:

GIVEN BY:- 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

●here ,

(i) 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,

here,

●(ii) LN = ½ SQ (By Mid point theorem) (Proved)

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