Allen WolmerSandy Springs, Georgia, US,

April 29, 2015

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- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10

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Table of Contents

- Identify and describe relationships among inscribed angles, radii, and chords.
- Explore the relationship between inscribed angles and central angles and their intercepted arcs.
- Prove the inscribed angle theorem, etc.
- Use the inscribed angle theorem to find the measures of unknown angles. Prove relationships between inscribed angles and central angles.
- Students discover that a line is tangent to a circle at a given point if it is perpendicular to the radius drawn to that point.
- Students use the inscribed angle theorem to prove other theorems in its family
- Inscribed Angles in Circles

Teacher Resources

Exercises from Illustrative Mathematics

A set of 8 exercises, commentary, and solutions

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Teacher and Student versions of full lesson from engageNY

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Prove the inscribed angle theorem: The measure of a central angle is twice the measure of any inscribed angle that intercepts the same arc as the central angle.

Recognize and use different cases of the inscribed angle theorem embedded in diagrams. This includes recognizing and using the result that inscribed angles that intersect the same arc are equal in measure.

Teacher and Student versions of full lesson from engageNY

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Teacher and Student versions of full lesson from engageNY

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Students discover that a line is tangent to a circle at a given point if it is perpendicular to the radius drawn to that point.

Students construct tangents to a circle through a given point.

Students prove that tangent segments from the same point are equal in length.

Teacher and Student versions of full lesson from engageNY

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Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays is tangent).

Students solve a variety of missing angle problems using the inscribed angle theorem.

Teacher and Student versions of full lesson from engageNY

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What if your family went to Washington DC over the summer and saw the White House? The closest you can get to the White House are the walking trails on the far right. You got as close as you could (on the trail) to the fence to take a picture (you were not allowed to walk on the grass). Where else could you have taken your picture from to get the same frame of the White House? Where do you think the best place to stand would be? Your line of sight in the camera is marked in the picture as the grey lines. The white dotted arcs do not actually exist, but were added to help with this problem. After completing this Concept, you will be able to use inscribed angles to answer this question.

Lesson, videos, exercises, and text from CK-12.

Additional resources available at this site.

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