Question

In fig. 9.25,diagonals Ac and BD of quadrilateral ABCD intersect at O such that OB=OD.If AB=CD,then show that:-(i)ar(DOC)=ar(AOB)(ii)ar(DCB)=ar(ACB)(iii)DA||CB or ABCD is a parallelogram.​

Answer 1

Step-by-step explanation:

(i)In ∆AOB and DOC

OB=OD(GIVEN)

AB=CD(GIVEN)

/AOB=/DOC(V.O.A)

∆AOB=~∆DOC(SAS)

THEY BOTH WILL HAVE EQUAL AREAS

THEY BOTH HAVE EQUAL BASE AND SAME AREAS SO ABll CD

(ii) AREAS OF ACB AND DCB ARE EQUAL AS THEY BOTH ARE ON SAME BASE AND SAME ll's AB AND CD

(iii)ACB and DCB are on same base and have equal areas so DA ll CB