Question

AD is a median of a triangle ABC and Eis mid-point of AD Show
ar. (AEB) = ar.(ABC)​

Answer 1

Answer:

Let ABC be a triangle and AD is the median of ΔABC

E is the mid point of AD

To prove : ar(BED)=

4

1

.ar(ABC)

In ΔABC,

ar(ABD)=ar(ACD) ___________ (1)

In ΔABD, BE is the median

ar(ABE)=ar(BED) __________ (2)

Now, ar(ABD)=ar(BED)

= 2. ar (BED) ______ (3)

ar(ABC)=ar(ABD)+ar(ACD)

ar(ABD)=2.ar(ABD) using (1)

ar(ABC)=2.2.ar(BED) - (2)

ar(ABC)= 4.ar (BED)

∴ar(BED)=

4

1

ar(ABC)

Hence it is proved.