Reflection: Rigor Angles Inscribed in Circles - Section 3: Proving Case 1 of the Inscribed Angle Theorem

 

Before the CCSS I had taught the proof of the inscribed angle theorem, but I had only taught students how to prove the most convenient case: the one where the side of the angle goes through the center. 

With the focus on math practices that came with the CCSS, I now feel compelled to teach the proof of all three cases. Not because I feel all three cases are so important but because it is a more faithful representation of what mathematicians actually do and how mathematics is as a discipline. To not include all the cases is to not be rigorous. It is to leave room for there to be cases in which what we are trying to prove is not true. Thinking in this way, we have to reason about all possible cases and try to put them into categories that are exhaustive. In this way, we're teaching more than the content, we're teaching the discipline. That was an 'Aha!' moment for me in this lesson.

 

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Angles Inscribed in Circles

Unit 8: Circles
Lesson 1 of 5

Objective: SWBAT Prove the relationship between the measure of an angle inscribed in a circle and the measure of its intercepted arc.

Big Idea: Inscribed angles prove not to be half bad...and students prove that they are half the measure of their intercepted arcs.

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Subject(s):
Math, Geometry, circles
  69 minutes
inscribed angle image
 
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