Q4 of 24 Page 252

What figure do you get, if you join ∆APM, ∆DPO, ∆OCN and ∆MNB in the example 3.

We get a figure like this



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2

ABCD is a parallelogram. AE is perpendicular on DC and CF is perpendicular on AD.

If AB = 10 cm, AE = 8 cm and CF = 12 cm. Find AD.


 3

If E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar(EFGH) ar(ABCD).

5

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD show that ar(∆APB) = ar ∆(BQC).

 6

P is a point in the interior of a parallelogram ABCD. Show that

(i) ar(∆APB) + ar(∆PCD) ar(ABCD)


(ii) ar(∆APD) + ar(∆PBC) = ar(∆APB) + ar(∆PCD)


(Hint : Through P, draw a line parallel to AB)