Abcd is a parallelogram x and y are midpoints
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ABCD is a parallelogram . X and Y are the midpoints of the opposite sides AB and CD respectively. Prove that AXCY is a parallelogram.
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Given: X and Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD.
AX = XB and DY = YC
To Prove: PXQY is a parallelogram.
Proof: AB = DC
... AB =  DC
XB = DY......(i)
Also AB ïï DC...... (opp. sides of a ïïgm)
XB ïï DY.....(ii)
Since in quadrilateral XBYD, XB = DY and XB ïï DY
... XBYD is a parallelogram.
... DX ïï YB ⇒ PX ïï YQ......(iii)
Similarly we can prove, PY ïï XQ ......(iv)
From (iii) and (iv), we get PXQY is a parallelogram.
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