Unit 9 · Circles

9.4Inscribed Angles

Quick Answer

Inscribed Angle Theorem: an inscribed angle is half its intercepted arc. Corollaries: inscribed angles that intercept the same arc are congruent; an angle inscribed in a semicircle is 90°.

Essential Question

Why is an inscribed angle always half the measure of its intercepted arc, and what special cases does this create?

Learning Goals

  • 1State the Inscribed Angle Theorem.
  • 2Apply the theorem to find inscribed angle measures.
  • 3Apply the corollary for angles in a semicircle.
  • 4Apply the corollary for angles intercepting the same arc.

Key Vocabulary

Inscribed angle

An angle whose vertex is on the circle and whose sides are chords.

Inscribed Angle Theorem

An inscribed angle equals half its intercepted arc.

Inscribed in a semicircle

An inscribed angle that intercepts a semicircle is a right angle.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.