Question

xyzw is parallelogram A is the midpoint
of side xy and
and B is the mid point of side
W Z prove that r XABW and ABZY
are paralleograms.



guys please help me ​

Answer 1

Step-by-step explanation:

ABCD is a parallelogram where X and Y are the midpoints of BC and CD. respectively. Prove that ar(triangle AXY) =(3/8) ar (ABCD).

Draw XM parallel to AB, so M is midpoint of AD. Also draw YN parallel to AD, so N is midpoint of AB.

Ar (triangle AXY) = Ar(ABCD) - ar(ABX) - ar(ADY) - ar(XYC)_

ar(ABX) = (1/2) of parallelogram ABXM = (1/4) Ar(ABCD)

ar(ADY) = (1/2) of parallelogram ANYD = (1/4) Ar(ABCD)

ar(XYC)_= (1/2) of parallelogram OXCY = (1/8) Ar(ABCD)

Therefore, Ar (triangle AXY) = Ar(ABCD) - (1/4) Ar(ABCD) - (1/4) Ar(ABCD) - (1/8) Ar(ABCD) = Ar(ABCD)[1 - (1/4) - (1/4) - (1/8)] = Ar(ABCD)[8-2-2-1]/8

= (3/8) ar (ABCD). Proved.