## 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.

Mathematical Practices not on the list
Rigor: Mathematical Practices not on the list

# Angles Inscribed in Circles

Unit 8: Circles
Lesson 1 of 5

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

Print Lesson
3 teachers like this lesson
Standards:
Subject(s):
Math, Geometry, circles
69 minutes

### Anthony Carruthers

##### Similar Lessons

###### NPR Car Talk Problem - Day 1 of 2
12th Grade Math » Trigonometric Functions
Big Idea: This problem from NPR's Car Talk is engaging, challenging, and mathematically rich!
Favorites(9)
Resources(19)
Troy, MI
Environment: Suburban

###### Circles are Everywhere
Geometry » Circles
Big Idea: This lesson asks students to create real circles and then review key vocabulary connected with circles like diameter, radius, center, secant, tangent and center.
Favorites(31)
Resources(24)
Saratoga Springs, NY
Environment: Suburban

###### End of Year Assessment
Geometry » Final Assessment
Big Idea: This is a comprehensive assessment of all content learned to date.
Favorites(1)
Resources(12)
New York, NY
Environment: Urban