(Q3) Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point 'O'. If AB = 2CD, find the ratio of areas of triangles AOB and COD.

Solution :

In trapezium ABCD, AB ∥ DC also AB = 2CD.

In ∆AOB and ∆COD

∠AOB = ∠   (vertically opposite angles)

∠ = ∠OCD   (alternate interior angles)

∆ ∼ ∆ (by AA Similarity)

ar(∆AOB)

ar(∆COD)

=

AB²

DC²

=

()

()

=

∴ ar(∆AOB) : ar(∆COD) = :