Question

D is the midpoint of the side BC of triangle ABC and E is the midpoint is BD . If O is the midpoint of AE, then prove that ar(triangle BOE)= 1/8 ar triangleABC)

Answer 1

Hey buddy your answer:

Since AD and AE are medians of ▲ABC and ▲ABD respectively.

Therefore,

ar. (▲ABD)=1/2 ar. (▲ABC).... (1)

and,ar. (▲ABE)=1/2 ar. (▲ABD).... (2)

OB is median of ▲ABE.

Therefore,

ar. (▲BOE)=1/2 ar. (▲ABE)........ (3).

From (1), (2) and (3),we have:

ar. (▲BOE)=1/8 ar. (▲ABC).

Hence,proved.

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