Question

In Fig. 8, and ΔDBC are on the same base BC and on opposite sides of BC ad Q is the point of intersection of AD and BC.

Prove that $\frac{area(\Delta ABC)}{area(∆DBC)}=\frac{AO}{DO}$

Answer 1

We have given the diagram in which

We have to prove that

Firstly, we draw a line from A perpendicular to line BC and after that we draw a line from D perpendicular to BC.

From the above figure we can easily see that theand are similar

Therefore by the properties of similar triangle, we have

…… (1)

Now,

From equation (1), we get

Hence proved.