In the adjacent figure ABCD is a parallelogram Pand Q arethe midpoints

1.	In the adjacent figure ABCD is a parallelogram Pand Q arethe midpoints of sides AB and DC respectively. Show thatPBCQ is also a parallelogram.
Answer» From the diagram attached with this answer, ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively . Since ABCD is a parallelogram,AB ║ CD and AB = CD P and Q are the mid points of AB and CD so, QC = 1/CD =1/AB = PB ie. QC = PB Also PB ║ QC and QC = PB then we get, PQ = BC Therefore PBCQ is also a parallelogram.

In the adjacent figure ABCD is a parallelogram Pand Q arethe midpoints of sides AB and DC respectively. Show thatPBCQ is also a parallelogram.

Answer»

From the diagram attached with this answer,

ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively .

Since ABCD is a parallelogram,AB ║ CD and AB = CD

P and Q are the mid points of AB and CD

so, QC = 1/CD =1/AB = PB

ie. QC = PB

Also PB ║ QC and QC = PB then we get, PQ = BC

Therefore PBCQ is also a parallelogram.