Question

D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar (Δ BOE) = $\frac{1}{8}$ ar (Δ ABC).

Answer 1

Given: In ΔABC

(1) D is the midpoint of the side BC

(2) E is the midpoint of the side BD

(3) O is the midpoint of the side AE

To prove:

Proof: We know that the median of a triangle divides the triangle into two triangles of equal area.

Since AD and AE are the medians of ΔABC and ΔABD respectively. And OB is the median of ΔABE

…… (1)

…… (2)

…… (3)

Therefore

Hence we have proved that