Q. 64.0( 4 Votes )

# In a trapezium ABCD, AB || CD and its diagonals meet at point O. If AB = 6 cm and DC = 3 cm then the ratio of the areas of ΔAOB and ΔCOD will be:

A. 4 : 1

B. 1 : 2

C. 2 : 1

D. 1 : 4

Answer :

In ΔAOB and ΔCOD,

∠O = ∠O |vertically opposite angle

As AB||CD

∠BAO = ∠OCD |alternate ∠s

∠OBA = ∠ODC |alternate ∠s

Thus, ΔAOB~ΔCOD

For two similar triangles, the ratio of their area is equal to the square of the ratio of their corresponding sides.

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