Question

a) In parallelogram ABCD, two points X and Y are taken on diagonal AC such that AX-CY. Prove that
(DAADX = ABYC (1) DX-BY.
D​

Answer 1

Answer:

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Since BXDY is a parallelogram .

∴ XO = YO --- (i)

DO = BO --- (ii)

[∵ diagonals of a parallelogram bisect each other ]

But AX = CY --- (iii) [given]

Adding (i) and (iii) , we have

XO + AX = YO + CY

⇒ AO = CO ---(iv)

From (ii) and (iv) , we have

AO = CO and DO = BO

Thus, ABCD is a parallelogram , because diagonals AC and BD bisect each other at O.

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