ABCD is a parallelogram in which X and Y are the mid points of AB and DC respectively. If AY and DX intersect in P while CX and BY intersect in Q, show that quadrilateral PXQY is a parallelogram.


Asked by Topperlearning User | 9th Dec, 2013, 02:35: AM

Expert Answer:

AB||DC
AX||YC
AB = DC        
AX = YC
 AX||YC and AX = YC
AXCY is a parallelogram.
AY||XC or PY||XQ
Also AB = DC
 XB||DY and XB = DY
XBYD is a parallelogram
XD||BY or XP||QY
Thus, PY||XQ and XP||QY
PXQY is a parallelogram.

Answered by  | 9th Dec, 2013, 04:35: AM