Education Technology

Central versus Inscribed Angles in Circles

Activity Overview

Using Cabri Jr. to explore the connection between central and inscribed Angles along with their arc measure.

Before the Activity

1. Load CIRCNIN to all student calculators. If not possible, make sure that the figure if projected and have a student use the teacher calculator to demonstrate the activity. 2. Students need to have an understanding of central angles and that the intercepted arcs of central angles have the same measure as the central angles. 3. Also, they need to be able to be able to recognize an inscribed angle, but do not need to know any more information.

During the Activity

1. Review what central and inscribed angles look like. 2. Have students run Cabri Jr. and bring up the file CIRCNIN using (F1 ?? Open) 3. Have the students examine figure. Allow any conjectures to be made. If none, ask if there is a relationship between the central angle and the inscribed angle. 4. Have students rotate point B around the circle. (Use the alpha button to grab the point, and then use the crosshairs.) What happens to the angles on the top right and left of the screen? Why? [If no responses make sure that the students realize that since the intercepted arc has not changed, the angle can not change.] 5. Now move either point A or C. Do not go past forming a diameter, because the limitation of Cabri jr is that it measures the inside of the angle. See what student observations will be made. 6. Get the group to form a diameter between the points A and C(180 degrees). What happens to the inscribed angle? Why is this powerful? [All right triangle properties, semicircle properties, etc.] 7. Close the activity by cleaning up the properties of inscribed angles.

After the Activity

Review student answers:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary