P and Q are the mid-points of the opposite sides AB and CD of parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

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Q. Question 7
P and Q are the mid – points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.

ABCD is a Parallelogram is which P and Q are mid-points of apposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that
(i) APCQ is a Parallelogram
(ii) DPBQ is a parallelogram
(iii) PSQR is a parallelogram
[3 MARKS]

Q. ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD . If AQ intersects DP at S and BQ intersects CP at R, show that ;
i) APCQ is a parallelogram
ii) DPBQ is a parallelogram
iii) PSQR is a parallelogram

Q. ABCD is a parallelogram. P is the mid-point of AB and R is the midpoint of DC as shown in the figure. Lines AR and DP intersect at S and lines PC and BR intersect at Q. Show that PQRS is a parallelogram.

E

is a point on the side

A D

produced of a parallelogram ABCD and

B E

intersects

C D

F .

Show that

△ A B E \sim △ C F B

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