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

Fill in the Blanks

The image shows a circle with chords CD, CB, ED and EB. The highlighted arc from point C to point E measures 100 degrees. The highlighted arc from point D to point B measures 140 degrees.

Prove that triangles CFD and EFB are similar.

Fill in the Blanks

The measure of the arc from B to A not passing through C is 30 degrees.

What is the measure of angle BOA?

Fill in the Blanks

The measure of the arc from B to A not passing through C is 30 degrees.

What is the measure of angle BDA?

Fill in the Blanks

The measure of the arc from B to A not passing through C is 30 degrees.

What is the measure of angle BCA?

• 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