This will drive you nuts for a while!

[GregW]

(Courtesy of http://www.ebaumsworld.com)

[qanda]

1. Kick

:kick:

Do you want to explain it? This is driving me nuts.

[Commie Pinko Dirtbag]

2. The big picture isn't really a triangle:

Proportions of the dark green triangle's cathets: 5/2 = 2.5
Proportions of the red triangle's cathets: 8/3 = 2.6666...

So the "big hypotenuse" isn't really a straight line. It's slightly bent down in the first picture, and slightly bent up in the second.

[LynneSin]

3. The 2 triangles aren't exactly the same size

take a look at the bottom triangle starting with the smaller dark green triangle on the left. That triangle is exactly 2 squares high to the mark.

Now check out the above triangle at the same position in the bigger red triangle (just following the grid straight up from the lower triangle to the upper one), it's not exactly 2 squares high at that point, it's just shy.

If you were to lay the top triangle directly on top the lower triangle you'll notice that the lower triangle is just ever so slightly larger. That extra space equals the extra square you see on the bottom triangle.

[Elidor]

4. Very good

It's a mathematical straw man. It's a fallacy to force shapes with more than three sides to the rules of three-sided shapes.

[Endangered Specie]

5. Although its hard to see, those are REALLY triangles...

The slope of the green triangle is 2/5 (rise/run) .40

The slope of the red triangle is 3/8 (rise/run) .375

Each side of a triangle is supposed to have the same slope...its a bit of an optical illusion.

(notice it doesn't say they ARE triangles, though they are meant to look like them. Each figure has the same area)

[WannaJumpMyScooter]

6. simple it is not the size or the height of the triangles, but the

length along the base
because you swapped the red and green triangles, you had to move the tan piece down one and over three, which leaves the gap seen below.

Also, I think mathematically it would be 8-5=3 which is the run of the x axis of both green and red segments which equal the squares of the tan had to move over. Since it only has two squares in that plane, you have a hole.