Suppose you have a triangle(x1,y1,x2,y2,x3,y3) and another one (x11,y11,x22,y22,x33,y33) . Coordinates don't come in a specific order.

The question: Can you draw the second triangle by just moving or rotating the first one? You can't detach the triangle from the board. EX: Therefore, using any of this two triangles you can't draw the other one.

So, one way is to compare the area and the angles, but still can't figure out how to deal with the case given above (where the area and the angles are equal, but the answer is still "NO". Maybe it's a special use of signed area formula?