When Scarecrow gets his ~~brain~~ diploma in *The Wizard of Oz*, he boldly and confidently states:

The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.

followed by "Oh joy! Rapture! I've got a brain!" ... or does he?

Is Scarecrow's Theorem *ever* true? If so, give an example. If not, show why.