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 =?

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/RbyD...



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.

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 =?
b
Reply:A) NO
Reply: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.
Reply:yes,but only if the triangle is equilateral