Education Technology

Relationship of Angles to the Circle

Published on 06/09/2008

Activity Overview

In this activity, students recognize the relationship of angles to its circles. They study the Inscribed Angle Theorem and its corollaries.

Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

  • TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
  • TI-Navigator™  "send to class" feature
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 71 - 74 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Construct a circle
  • Draw two secants to create an inscribed angle (an angle formed by two secants whose point of intersection lies on the circle)
  • Measure the inscribed angle
  • Measure the arc opposite the inscribed angle (intercepted arc)
  • Observe that the measure of the inscribed angle is half the measure of the intercepted arc
  • Alter the angle and verify the relationship


  • Construct a circle
  • Draw two secants to create an interior angle (an angle formed by two secants that intersect inside the circle)
  • Measure the interior angle
  • Measure the arcs intercepted by the angle
  • Observe that the measure of the interior angle is half the sum of the measures of its intercepted arcs
  • Alter the angles and verify the observations


  • Construct a circle
  • Draw two secants to create an exterior angle (an angle formed by two secants that intersect outside the circle)
  • Measure the exterior angle
  • Measure the intercepted arcs
  • Observe that the measure of an exterior angle is half the difference of measures of its intercepted arcs
  • Alter the angles and verify the relationship
  • After the Activity

    Review student results:

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