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can anyone explain y this works?

The ?hypoteneuse? of the triangle is slightly bent in, in the top one, and slightly bent out in the second one, just enough for one square. The thick line obscures that fact. Optical illusion
 
Look at the hypotenuse of the two, you will see that at each horizontal mark, the triangle on the bottom is taller than the one at the top...
 


<< the angle of ascent changes. >>



exactly. It works because it's not a traingle.

the big peice is 8 units wide by 3 units tall. The small peice is 5x2. If this was a triangle, those two ratios would have to be the same, but 8/3 != 5/2.
 
Here is a mathematical attempt at explaining it (hope you can follow simple y=mx+b) 😛

Whole Triangle:
It is close to a classic 12base)x5(hieght)x13(hypot) triangle.

Easiest way to prove that the hypotonuse of both triangles isn't straight is from calculation of slopes.

Slope for green triangle: 2 / 5 = 0.4
Slope for red triangle: 3 / 8 = 0.375
Slope for (real) triangle: 5 / 12 = 0.41666...

To the naked (read "nikked") eye, it looks like the hypotenuse is straight.

EDIT: Fixed classic triangle measurements.

 
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