Question

E is the mid point of AD. prove that ar(∆BEC) =1/2 ar (∆ABC)

Answer 1

Given: E is any point on median AD of a Δ ABC.

To Prove: area(Δ ABC) = area(Δ ACE).

Proof: In Δ ABC,
AD is a median.

∴ area(Δ ABD) = area(Δ ACD) ….(1)

In Δ EBC,
ED is a median.

∴ area(Δ EBD) = area(Δ ECD) …..(2)


Subtracting (2) from (1), we get


area(Δ ABD) – area(Δ EBD) = area(Δ ACD) – area(Δ ECD)


⇒ area(Δ ABE) = area(Δ ACE).

Using this we can prove ar(ΔBEC)=1/2 ar(ΔABC).