Why is a Square a Rectangle?

My daughter and I were looking at shapes counting rectangles amid a bunch of triangles and circles.  One rectangle looked a bit more like a square then the others so she didn't count it.  She said that is a square not a rectangle.  I then explained, "Actually, squares are rectangles and so you would count the squares."  My daughter lost it.  It was like I had told her that the world really is flat.  She started crying and crying out, "No, they are not!"

I was lost myself at to how to explain then I found two websites.

Geometry: Basic Ideas
Ask Dr. Math

I think she would still rather not believe it but maybe when it comes up in Math the next time she will be ready to accept it as fact.