Education Technology

Circles - Angles and Arcs

Updated on 08/14/2014

Activity Overview

Investigate inscribed angles, central angles and intercepted arcs relationships in circles.

Objectives

  • Students will know the definitions of 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.

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.