Inscribed Angle Theorem

Inscribed Angles

Let’s analyze angles made from chords.

• I can use the relationship between central and inscribed angles to calculate angle measures and prove geometric theorems.

• I know that an inscribed angle is half the measure of the central angle that defines the same arc.

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​Learning Targets

Open Ended

Name the central angle in this figure.

An inscribed angle is an angle with its vertex on the circle and whose sides are chords

​inscribed angle

Open Ended

Name the inscribed angle in this figure.

The minor arc of a circle that lies between two lines that intersect it.

​Intercepted arc

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

​Inscribed Angle Theorem

​https://im.kendallhunt.com/HS/students/2/7/2/index.html

Inscribed angles that intercept the same arc are congruent. This is called the Congruent Inscribed Angles Theorem and is shown below.

Congruent Inscribed Angles Theorem

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• I can use the relationship between central and inscribed angles to calculate angle measures and prove geometric theorems.

• I know that an inscribed angle is half the measure of the central angle that defines the same arc.

​

​Learning Targets