# 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

**Solution:**

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

AA criterion.

In trapezium ABCD,

AB is parallel to CD and AB = 2 CD

Diagonals AC and BD intersect at ‘O’

In ΔAOB and ΔCOD

∠AOB = ∠COD (vertically opposite angles)

∠ABO = ∠CDO [alternate interior angles]

⇒ ΔAOB is similar to ΔCOD (AA criterion)

⇒ Area of ΔAOB / Areaof ΔCOD = (AB)^{2 }/ (CD)^{2} [theorem 6.6]

(2CD)^{2} / (CD)^{2} = 4CD^{2} / CD^{2} = 4 / 1

⇒ Area of ΔAOB : Area of ΔCOD = 4:1

**Video Solution:**

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

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.4 Question 2:

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

Diagonals of a trapezium ABCD with AB || DC intersect each other at the point If AB = 2 CD, the ratio of the areas of triangles AOB and COD is 4:1