Reply #16: First of all they are NOT triangles. [View All]

[Systematic Chaos]

It's an optical illusion.

They first pic actually shows a quadrilateral with an unmarked point where the two triangles meet. This is because, as already explained, the slopes of those two line segments are NOT THE SAME. Your eyes might tell you they are, but they arent, so AB is not actually a line, so ABC, by definition, is NOT a triangle.

It would be like taking a perfect square of x units per side, cutting it into several irregular shapes, and then wondering why you don't get a square when you rearrange those random shapes in a different fashion.

The sum of the areas of the shapes in both diagrams is the same, yes, but the assumption that ABC is a triangle is false; in fact, it is impossible to form an actual triangle from the pieces which constitute ABC.

Now do you understand?