The Curry Triangle paradox is based on two non-similar triangles.
The two right triangles appear to be similar (and interchangeable),
. . but they are not.
If they were similar right triangles, they would have a common hypotenuse.
(Designated o - o - o - o ...)
..o:::::::* - - - *
..o:::::* | 5
* - - - - - - - - - - - *
In the first diagram, the two triangles fall below the common hypotenuse.
Their area is short by exactly one-half a square unit.
* - - - o - - - - - - - *
.*:| o 8
o - - - *
In the second diagram, the triangle are partly above the common hypotenuse.
Their area is over by exactly one-half a square unit.
And that is the basis of the paradox.