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

Question

Philoid · Accepted Answer

Since AB || CD,

∴∠OAB = ∠OCD and ∠OBA = ∠ODC (Alternate interior angles)

In ΔAOB and ΔCOD,

∠AOB = ∠COD (Vertically opposite angles)

∠OAB = ∠OCD (Alternate interior angles)

∠OBA = ∠ODC (Alternate interior angles)

ΔAOB ~ΔCOD (By AAA similarity)

Since, AB = 2 CD

Therefore,

Therefore, the ratio of the areas of triangles AOB and COD is 4:1