Question

please solve this.............

Answer 1

given that'

abcd is a parallelogram
p and q are the midpoints of ab and dc

to prove apqd is also a parallelogram

proooof:

since abcd is a parallelogram ab and bc are equal             
because opposite sides of a parallelogram are equal.

since q and p are the midpoints of the parallelogrm abcd
if we join pq
it becomes the median of the parallelogram

hence it divides the parallelogram into two equal parallelogram

hence apqd is also a prallelogram.

Answer 2

given...
ABCD is a parallelogram..
now..P and Q are mid points of AB and CD so that...
to prove....
APQD is a parallelogram..

prof...
Join the diagonal AC ....
such that it forms two triangles .....
now ...
name the intersection of AC and PQ as O
let...
PO is parallel to BC....
hence by using thales theorem...
AP/PB=AO/OB...
again..
We get that O is the mid point of AC
so line drawn from mid point to another mid point in a triangle is parallel to the third side..
so...AO/OB=DQ/QB
Hence..AB parallel to PQ parallel to BC...
so APQD is a parallelogram
proved....