How can this be true?
When re-arranged there is a square missing, spooky.
I don’t get it
This is creepy, If any one is good at geometry PLEASE explain this.
there is a rational explanation for that but for the life of me…
III know the secret 
no, just kidding, I don’t. I’ve seen that picture before, tried to figure it out, but now I’ve just accepted that it’s magic.
I’m going to print this off and show it to some of my friends. I can just see the look on their faces…
That’s a good one! Can anyone explain what’s going on here??
Thanks for the answer! My mind was about to explode. I actually printed it out and cut out all shapes and still couldn’t figure it out. It sure is a tricky little thing isn’t it…
I dont get whats so tricky…the little L shapes are just uneven, thats all.
What do you mean by uneven? They are the same shape and size?
look at how much space (how many squares) the top triangle takes up. then compare it to the bottom one. they take up exactly the same area, except for one square is missing.
My head feels better now.
Thanks for the explanation.
The simplest explanation i can see is this, the hypotenuse of the overall triangle is not a straight line i.e the hypoteneuse of the two triangle pieces are not parallel. The simplest to notice manifestation of this is: look at the left hand point of the overall shape, count five squares to the right, go up till you hit the hypotenuse of the overall shape, on one figure this point is exactly at an intersection of the grid, on the other it’s very slightly below i.e. they have the same area but are not the same shape. If you had these pieces CNC machined in steel to a large scale the gaps and differences would be quite noticeable, but in paper they’re eaten up by inaccuracies in cutting out etc.
That’s right, one triangle’s sharp angle has a ‘tangent’ of 2/5 = 0.40, the other has 3/8 = 0.375. BTW, this thing has been posted before in JC.
Klaas Bil
LOL, when I saw this thing years ago, I had the same drive to solute it. Untill I was using a CAD-like drawing program (and found out what was going on), it drove me crazy!
non-congruent triangles
That is über-obvious; one is less than half the surface area of the other. You mean they have not the same shape?
Klaas Bil
Not meaning to be argumentative (since I am usually wrong when I am convinved I am right), but which triangles do you mean are non-congruent? Both the red triangles are the same, and so are both the green ones. The problem is that the large “triangles” are not triangles, but quadrilaterals.
below is supposed to be an extreme example of the top of the two “triangles”
/ ____
____/ /
/
thus the second one has more area, allowing there to be an empty space.
edit: well, that didn’t work, I guess I will have to work on my formatting skills.
as yooper linked earlier, it’s because the triangles are slightly different when overlapped. the one without the square is bowing out by an area of 1 square, but spraed across the hypotenuse so it doesn’t seem obvious.
the end
… and therefore you must have meant something else; sorry for jumping to conclusions. You probably meant the larger ones. Like sevenasterisks pointed out, they are not triangles but that is not über-obvious.
Klaas Bil