I’ve had success with students when we are first learning all the geometric objects involved with circles by writing out the name, definition, symbol, and diagram for all the parts. I’ve heard some teachers comment on the difficulty students face keeping track of it all. and so many relationships between the measures of angles, arcs, and various segments. There are many new terms that students learn when they study circles: radius, diameter, chord, secant, tangent, arc, etc. I think this would be a wonderful way to start the school year, sending a message to students that they will be doing math not viewing math, and that surprising results can spur us onward to better conceptual understanding. What a surprise to find out that everyone in his class got the same result, changing the question from “What do we know” to “ How do we know it?” As a 10-year-old, he assumed that the measure of the angle depended on the location chosen for the point on the semicircle. This is such a wonderful result – think about the ways you might justify why this is true – and a great opportunity to have students discover this invariant for themselves.*ĭavid Acheson describes this as the introduction in “The Wonder Book of Geometry”. The third way right angles appear in circlesis that any angle inscribed in a semicircle will be a right angle (Thales’ theorem).
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