Missing square puzzle

Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square
Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid.

The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle, but one has a 1×1 hole in it.