# Inscribed Angle Theorem

- Author:
- Ashley Dugas, Tim Brzezinski

- Topic:
- Angles

**Students:**The directions for this activity can be found below the applet.

## Step 1

**Ray**tool to construct the following: Ray with

**endpoint**that passes through

*B***Ray with**

*A*.**endpoint**that passes through

*B*

*C*.## Step 2

**vertex**you've just constructed is said to be an

*B***inscribed angle of the circle**. This

**inscribed angle**is said to intercept

*B***arc**. Use the

*AC***Angle**tool to find and display the measure of this inscribed angle.

## Step 3

**Ray**tool to construct the following: Ray with

**endpoint**that passes through

*O***Ray with**

*A*.**endpoint**that passes through

*O*

*C*.## 4.

Recall that this angle you've just constructed in the previous step is called a **central angle **of the circle.
**How does the measure of this central angle compare with the ****measure of the blue arc** it intercepts?
Use the **Angle** tool to find and display the measure of this central angle.

**How does the measure of the inscribed angle compare with the measure of the central angle **that intercepts the **same arc**? (Feel free to move **points A** and

*around!)*

**C**## 7.

Click the **Show Other Point** checkbox to display another point (**point D**) on the

**pink arc**. Then create an inscribed angle with

**vertex**that intercepts

*D***arc**. Then measure this angle. What do you notice?

*AC*## Inscribed Angle Theorem

Complete the following statements:
*A central angle is*_______________the measure of the intercepted arc.
*An Inscribed Angle is *_________________the measure of its intercepted arc.