Question

ABCD is a parallelogram and X and Y are the mid points of sides AB and DC respectively.show that AXCY is a parallelogram

Answer 1

By this method AXCY is a parallelogram

Answer 2

Given,

ABCD is a parallelogram, X and Y are the midpoints of sides AB and DC respectively.

To find,

We have to prove that AXCY is a parallelogram.

Solution,

We can simply prove that AXCY is a parallelogram by using the properties of a parallelogram.

AX = BX and DY = CY (x and y are the midpoints of AB and DC)

AB║DC then,

AX║CY and AX = CY

Hence, AXCY is a parallelogram.