Question

Diagonal AC and BD of a quadrilateral ABCD intersect at O such that OB = OD . If AB = CD then show that , 1. ar(AOB) = ar(DOC)
2. ar(DCB) = ar(ACB) 3. DA || CB or ABCD is a parallelogram. QUICK PLZ ....

Answer 1

Given
abcd is a quadrilateral
in which ac and bd are diagonal and intersect at o

construction. ..
join ac and bd
proof
ar (aob)=ar (ocd)

da ||cb and ac is a transversal
to prove. . abcd is a parallelogram
again proof


angle aob = angle cod (opp angle )
ab=cd given



triangle oab =~ triangle ocd (by sas)
angle oab=angle ocd (by cpctc)
so oa=oc
ob=od
angle aod=angle ocb
so
triangle oad =~triangle obc ad=bc
angle oad =angle ocb( by sas ) and cpctc
ad||bc ( from equal alternate)
lly...
ad || dc
abcd is a parallelogram
if it is helpful so mark as brainiest

Answer 2

Plz mark as brainliest the other answer..