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
pradeep says
Good