Question

e is the mid point of the median ad of triangle abc. prove that ar(abe)=1/4of abc

Answer 1

GIVEN➡E is the midpoint of AD

➡To Prove->ar(∆ABE)=1/4ar(∆ABC)

➡construction-->Join BE and CE

➡proof--->In triangle ABD

since BE is also a median

Therefore ar(ABE)=ar(BED)=1/2ar(ABD)

[As median of a triangle divides it into two equal areas]

2ar(ABE)=(ABD)---------------------------1.)

since ar(ABD)=1/2(ABC)

[ As AD is also a median thus we can say that median of a triangle divides it into two equal areas]

➡2ar(ABE)=1/2(ABC) [From eq. 1]

➡ar(ABE)=1/4ar(ABC)

.......Hence proved