In the spirit of Post's theorem on triangles, we find a necessary and sufficient condition on the sides s of a square and a, b, c of a triangle for the square to fit into the triangle.

More generally, we give a necessary and sufficient condition on the sides u, v of a rectangle and a, b, c of an acute (or right) triangle for a u x v rectangle to fit into a triangle with sides a, b, c. The corresponding problem for an obtuse triangle has not yet been analyzed.