Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Geometry and Trigonometry

Circles: Angles and 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