**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 2**

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

**Solution:**

**Given:** ABCD is a trapezium with AB || DC where AB = 2CD

In and

{Alternate Interior Angles as AB || DC}

{Vertically Opposite Angles}

Therefore, by **AA similarity criterion**, ~

**(1)**

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

But, we also have AB = 2CD **(2)**

Putting equation **(2)** in **(1)**, we get

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