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.