In , D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of .

We have, D and E as the midpoint of AB and AC

So, according to the midpoint therom

DE||BC and DE = 1/2 BC……………..(i)

In ΔADE and ΔABC

<A = <A (Common)

<ADE = <B (Corresponding angles)

Then, ΔADE ~ ΔABC (By AA similarity)

By area of similar triangle theorem

Area ΔADE/ Area ΔABC = DE²/BC²

Or, (1/2BC)²/(BC)²

Or, 1/4