Recent content by Purplesquiggles

I can prove what you said quite easily. The only problem is that the converse, which is my initial question, remains unproved. I don't know for certain that 3 triangles of equal area must meet at the centroid. Its possible there are other places where this can occur. I have to prove the centroid...

You are given an arbitrary triangle ABC. Inside ABC there is a point M such that Area(ABM) = Area(BCM) = Area(ACM) . Prove that M is the centroid of triangle ABC. I have had very little progress with this question. I've tried connecting a line from M which bisects BC, but I cannot prove that...