One major task of the geometry teacher is to get your students to transition from recognizing geometric figures by “looks” to recognizing geometric figures by definition. I’ve found my students saying things like “a rhombus is a sideways diamond,” or “a trapezoid is the funny shaped one,” or “what do you mean ‘what’s a rectangle?’, it’s a rectangle!” Today everyone was stumped when I asked them to draw a rectangular rhombus, “If you wanted us to draw a square Mr. Follett, why didn’t you just ask!?”
Getting our students to a level of precision where they can say “yes, that’s a trapezoid because it has only one set of parallel sides” may seem trivial but it reflects a level of mathematical precision which has a profound effect on thinking. Our students can now move away from the “it is because it is” sort of line of argument to “it is because….” So we stop falling prey to persuasion with no “meat” and begin to think critically about the things which influence us and the things we believe.