CBSE Class 9 Answered

Const : Draw a line parallel to SR through M and a line parallel to SP through M

Proof : (i)

In parallelogram PQRS,

PQ || UV(by construction) ……(i)

PS || QR(opp. sides of a parallelogram)

Therefore, PU || QV……(ii)

From (i) and (ii),

PQ || UV and PU || QR

Therefore, quadrilateral PUVQ is a parallelogram.

It can be observed that PMQ and parallelogram PQVU lie on the same base PQ and between the same parallels PQ and UV

Similarly, for MRS and parallelogram SRVU,

adding (iii) and (iv)

(ii)

In parallelogram PQRS,

PS || XY(by construction) ……(vi)

PQ || SR(opp. sides of a parallelogram)

Therefore, PX || SY……(vii)

From (vi) and (vii),

PS || XY and PX || SY

Therefore, quadrilateral PSYX is a parallelogram.

It can be observed that PMS and parallelogram PSYX lie on the same base PS and between the same parallels PS and XY

Similarly, for MRQ and parallelogram XYRQ,

adding (viii) and (ix)

From (v) and (x)