Geometric Logic Puzzles

Is a square an equilateral rectangle? If two skis are parallel, are they still parallel if one of them breaks?

Our class has been engaged in a couple of interesting math discussions. One focused on how it is that you can call a square a rectangle, but you cannot call a rectangle a square. (This naturally flies in the face of our students' sense of fairness and logic!) The second discussion focused on whether lines (or in this case, sides of polygons) can be called parallel if one side is longer than the other (as in a classical trapezoid) or if one side "starts" before the other (as in a classical parallelogram). We broke a number of popsicle sticks in our quest for the truth!