Triangle ABC was divided into 4 figureswith areas S1,2,3,4 as in the fig. Is it possible for S1,2,3,4 to be =?

Question

Triangle ABC was divided into 4 figures with areas S1, S2, S3, S4 as shown in the figure. Is it possible for S1, S2, S3, S4 to be equal?

For fig see http://bp2.blogger.com/_fxxCUzKqoio/RbyDdeL7XMI/AAAAAAAAAAM/onKaUIWj0dE/s1600-h/Figure.jpg

A) No
B) Yes, but only if the triangle is equilateral.
C) Yes, but only if the triangle is a right triangle.
D) Yes, when the triangles has angles : 36º, 72º, 72º.

Please answer if you know.

Answer 1

b

Answer 2

It can only be No because such a property is preserved by any affine transformation which would not preserve angles or equality of lengths along different directions.

The fact is, if you want S1 + S2 = S3+S4 you need E to be the middle of BC and similarly for D. Hence you would have that the intersection is the center of gravity of the triangle and then
S2=S4=2S1=2S3.

Answer 3

yes,but only if the triangle is equilateral

Answer 4

A) NO