Question

in the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively . show that PBCQ is also a parallelogram.

Answer 1

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.

Answer 2

Step-by-step explanation:

ABCD is a parallelogram

P and Q are mid points of sides

AB and DC

AB||CD, AB=CD

SO, QC=1/CD=1/AD=PB

i.e OC=PB

PB||QC and QC =PB

then we get PQ=BC

therefore, we get

PBCQ is a paralellogram