Education Technology

Circles - Angles and Arcs

Updated on 05/10/2022

Activity Overview

In this TI-84 family activity, students explore angles constructed in a circle and how their measures are related to the measures of the intercepted arcs.

Objectives

  • Students will define and identify central angles, major and minor arcs, intercepted arcs, and inscribed angles of a circle. 
  • Students will determine and apply the following relationships:
    • Two inscribed angles intercepting the same arc have the same measure.
    • An inscribed angle measure of 90° results in the endpoints of the intercepted arc lying on a diameter.
    • The measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc.
    • Students will try to make a connection with how to understand these topics in IB Mathematics courses on their final assessments

Vocabulary

  • Central angle
  • Inscribed angle
  • Major arc
  • Minor arc
  • Intercepted arc

About the Lesson

This lesson involves manipulating endpoints of an arc, manipulating an inscribed angle, and manipulating the vertex of an angle intercepting an arc. As a result students will:

  • Use visualization to understand the definitions of central angle, intercepted arc, and minor and major arcs.
  • Infer that the sum of the measures of minor and major arcs is 360°, that two inscribed angles intercepting the same arc have the same measure, and that the inscribed angle has half the measure of the central angle that intercepts the same arc.
  • Deduce that the opposite angles of a quadrilateral inscribed in a circle are supplementary.