Question

E is the mid point of the median AD of a triangle ABC. show that ar(triangle ABE) = 1/4 ar(triangle ABC)

Answer 1

Explanation:

In triangle ABC

ABD=ACD-------------(1)

In triangle  abd,BE is the median

Abe = bed-------------(2)

Now,

ABD = BED

=2 (BED)-----------(3)

ABC=ABD + ACD

ABC = 2(ABD)----- using(1)

ABC =2 * 2(BED)---- using(3)

ABC = 4(BED)

So,

(BED) = 1/4(ABC)

Hope It's Helps!