# G.GCI.2 Inscribed Angle Theorem: Take 4!

- Author:
- Dan Dale, Tim Brzezinski

## DIRECTIONS:

In the GeoGebra applet below:
1) Use the SEGMENT tool to construct segments , , , and .
2) Use the ANGLE tool to measure and display the measure of and .
Then, answer the questions that appear below the applet.

## 1.

Immediately select the MOVE arrow. Then drag the angle measures to a place where you can see them clearly. What do you IMMEDIATELY NOTICE? Describe in detail in the space provided.

## 2.

Now drag the **BLUE DOT on the blue slider** to change the measure of the circle's** blue central angle**. (You can also enter any angle measure you wish).
Each **gray angle** is said to be an **inscribed angle** of this circle. Note that each gray inscribed angle intercepts the same arc (of the circle) as the **blue central angle**.
What do you notice about the **measures of the gray inscribed angles** with respect to the **measure of this blue central angle**?