Question

ABCD IS A PARALLELOGRAM WITH DIAGONALS AC AND BD MEETING EACH OTHER AT O .PROVE THAT AREA OF AOB +AREA OF DOC =1+2 AREA OF ABCD

Answer 1

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Let's take ABCD a square ( type of //gm)
AO=0C. ........* (DIAGONALS BISECT. EACH OTHER IN A //GM)
DO = OB. ............ (,,)
AB= DC .......... ( EQUAL SIDES OF A SQUARE)

So, AOB IS CONGRUENT TO DOC.

Similarly, AOD~DOC
SO, ar. AOB + ar. DOC= 2×2/4 = 1/2 ar. ABCD.

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