Students investigate the relationship between measure of central and inscribed angles in a circle.
Before the Activity
Pair students and give them calculators
During the Activity
1. Draw a circle
2. Locate 2 points on the circle.
3. Draw 2 segments from the 2 points to the center to form a central angle.
4. Measure the central angle.
5. Find a thrid oint on the far of the center from the other 2 points.
6. Use 2 segments to connect the first 2 points on the circle to the third point, forming an inscribed angle.
7. Measure the inscribed angle.
8. Grab the vertex of the inscribed angle and move the vertex around the circle.
9. What do you notice about the relationship of the measure of the inscribed angle and the central angle?
10. Grab one of the points on the circle of the central angle. Move the point around the circle.
11. Record 5 pairs of measurements of the incribed and central angles.
12. What relationship can you generalize between the measure of the inscribed and central angles?
After the Activity
Students record pairs of measurements and determine that central angle is equal to 2 times the inscribed angle.