Question

In the adjacent figure ABCD is a parallelogram Pand Q are the mid points of sides AB and DC respectively .Show that PBCQ is also aparallelogram

Answer 1

in a quadrilateral ABCD.
AP|| QC.( because AB||CD).
Hence,
AP= 1/2 AB.....(1)
CQ= 1/2 CD.( given)
also, AB= CD
so, AP= QC........(2).
therefore, ABCQ is a parallelogram.
[ from equation (1) and (2)]

Answer 2

P , Q are the mid points of AB and CD.

Join Q , P .

Now , AB = CD

[ Since , opposite sides of

parallelogram ]

AB/2 = CD/2

=> PB = QC

Also PB // QC

Now in Quadrilateral PBCQ ;

PB = QC ,

PB // QC

Hence , PBCQ is a parallelogram .