Question

In the given figure X and Y are the midpoint of AB and CD respectively of a parallelogram ABCD. Show that AXCY is a parallelogram ​

Answer 1

Answer:

ABCD is a parallelogram

=> AB=CD and AB=CD

(Since opposite sides are equal and and parallel in a parallelogram)

Now,

Since AB=CD

=>1/2 AB= 1/2CD

=>AX=CY

(Since X is the midpoint, AX is half of AB and Y is midpoint, CY is half of CD)

again,

Since AB || CD

=> AX || CY

(Because they are the part of AB and CD)

So now we have,

AX=CY

AX || CY

Since Opposite sides are equal and parallel, AXCY is a parallelogram.

Step-by-step explanation:

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