Inscribed Angle Theorems: Take 3!
Students:
The directions for this activity can be found below the applet.
1.
Use the Ray tool to construct the following:
Ray with endpoint B that passes through A.
Ray with endpoint B that passes through C.
Hint: Click on the ray/line tool (middle button at the top), then click on endpoint B and make the line go through point A. Repeat for endpoint B and point C.
2.
This angle with vertex B you've just constructed is said to be an inscribed angle of the circle. This inscribed angle B is said to intercept arc AC. Use the Angle tool to find the measure of this inscribed angle . (Click on the angle tool, then points A, B, and C). Write the angle measure below.
3.
Use the Ray tool again to construct the following central angle:
Ray with endpoint O that passes through A.
Ray with endpoint O that passes through C.
4.
Use the Angle tool to find the measure of this central angle . Write the measure below.
5.
How does the measure of the inscribed angle (#2) compare with the measure of the central angle (#5) that intercepts the same arc? (Feel free to move points A and C around!)
Find the inscribed angle measure. If = , what is the
Find the arc measure/central angle. If m