Points A and B lie in the same plane. How many isosceles right triangles in the plane have A and B as vertices?

A) Three

B) Four

C) Five

D) Six

E) Infinitely many

That side can be the hypotenuse of such a triangle on either side of it, and it can also be one leg of such a triangle in 4 orientations. Look:

The smaller, darker triangles are where segment *AB* is the hypotenuse. The larger triangles are the four other orientations.