disprove the following:
Imagine a triangle with corners A,B, and C
points D, E, and F are the centers of each if its sides.
now, draw line segments DF and EF (in your mind, or on your recently drawn triangle).
We know that DF=1/2BC=BE
Therefore, the sum of the lengths of line segments AD,DF,FE, and EC=AB+BC
if we repeat the above process in triangles ADF and FCE (here, again, the zig-zagged line is equal AB+BC), then repeat it again in the triangles created (here, again, the zig-zagged line is equal AB+BC), etc., the zig-zag lines will get closer and closer to AC, and finally join it. The length of that final zig-zagged line will be equal to AC, and, to AB+BC. Therefore, in any triangle, every one side (AC)will be equal to the sum of the others.