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

1.	In ΔABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
Answer» 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

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

Answer»

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