Once similarity intuition has been built with circles, we can start getting into more specific relationships with angles and segments. This post will look at using visual information from central angles and inscribed angles.
Students sometimes lack intuition for the measure of something. Andrew Stadel has developed this idea into a thorough curriculum on estimation. In my classes we started reasoning through similar exercises. Once we had a decent understanding of circle parts and whole, we moved on to other types of angles.
At this point most students have the common sense that a circle has 360 degrees, and a triangle is half that at 180 degrees. Built with this intuition in mind, we look at a triangle created by inscribed angles.
The next day we get to see the formula that collapses 3 ideas down to 1.
Dynamic Angles in…
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