In quadrilateral ABCD of the given figure, X andY are points on diagon

1.	In quadrilateral ABCD of the given figure, X andY are points on diagonal AC such that AX = CY andBXDY is a parallelogram. Show that ABCD is a parallelogram.
Answer» Step-by-step EXPLANATION: We have, BXDY is a parallelogram. Therefore the diagonals bisect each other =>BO=DO, XO=YO............. (1) Given, AX=CY. ADDING xo on both sides, we get, AX+XO=CY+YO.......... from 1 we have XO=YO AO=CO. SINCE AO=CO, BO=DO, therefore the diagonals bisect each other Or, ABCD is a parallelogram

In quadrilateral ABCD of the given figure, X andY are points on diagonal AC such that AX = CY andBXDY is a parallelogram. Show that ABCD is a parallelogram.

Answer»

Step-by-step EXPLANATION:

We have, BXDY is a parallelogram. Therefore the diagonals bisect each other

=>BO=DO, XO=YO............. (1)

Given, AX=CY.

ADDING xo on both sides, we get,

AX+XO=CY+YO.......... from 1 we have XO=YO

AO=CO.

SINCE AO=CO, BO=DO, therefore the diagonals bisect each other

Or, ABCD is a parallelogram

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In quadrilateral ABCD of the given figure, X andY are points on diagonal AC such that AX = CY andBXDY is a parallelogram. Show that ABCD is a parallelogram. ​

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In quadrilateral ABCD of the given figure, X andY are points on diagonal AC such that AX = CY andBXDY is a parallelogram. Show that ABCD is a parallelogram.