In figure X, Y are the mid points of sides AB and CD of a parallelogram ABCD AY - Maths - Quadrilaterals

Question

In figure X, Y are the mid points of sides AB and CD of a
parallelogram ABCD AY and DX are joined intersecting at P, CX and
By are joined intersecting at Q Show that PXQY is a
parallelogram

Vimala · Accepted Answer

Let us observe the following figure
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/4123631/2012_12_05_20_45_31/image1327875045345601832_1807054942099608923%20jpg">
Since X is the midpoint, AX = XB, Y is the midpoint, CY = YD
ABCD is a parallelo gram, therefore, AB = CD
Therefore, AX = CY
Also, AB is parallel to DC
Therefore, AX is parallel to CY
Thus, AXCY is a parallelogram
Consequently, PY is parallel to QX
Since X is the midpoint, AX = XB, Y is the midpoint, CY = YD
ABCD is a parallelo gram, therefore, AB = CD
Therefore, BX = DY
Also, AB is parallel to DC
Therefore, BX is parallel to DY
Thus, BXDY is a parallelogram
Consequently, PX is parallel to QY
Thus, the arguments are,
1 PY is parallel to QX
2 PX is parallel to QY
Therefore, PXQY is a parallelogram

In figure X, Y are the mid points of sides AB and CD of a parallelogram. ABCD. AY and DX are joined intersecting at P, CX and By are joined intersecting at Q. Show that PXQY is a parallelogram.