Education Technology

Relationship of Angles to the Circle

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