Question

diagnols of a trapezium
with AB II DC intersect each other at the point o
find the ratio of the areas of thangles AOB and COD
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Answer 1

given : ABCD is a trapezium where AB is parrel to CD and diagonals intersect at O.

AB=2CD

TO PROVE : ar. ∆AOB ÷ ar. ∆ COD

In Δ AOB and COD

∠DOC = ∠BOA [ vertically opposite angle via (V.O.A property )

∠COD = ∠ABO [alternate interior angle property ]

hence , ∠DOC = ∠BOA

now we can say that ΔAOB ≈ΔCOD

Area of triangle (AOB) : area of triangle COD =AB^2:CD^2

: area of triangle COD)=(2CD)^2:CD^2

area of triangle ( AOB) : area of triangle ( COD)=4CD^2:CD^2

area of triangle AOB : area of triangle (COD) = 4 : 1.