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Exploring Inscribed Angles: Theorem, Examples, and Corollaries

Learn about inscribed angles, their theorems, and examples in this comprehensive guide. Understand the relationship between angles and intercepted arcs on circles. Practice solving angle measurements with chord and tangent combinations.

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Exploring Inscribed Angles: Theorem, Examples, and Corollaries

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  1. 12.3 Inscribed Angles

  2. Vocab: inscribed angle -an angle whose vertex is on a circle and whose sides are chords <ABC and <DEF are inscribed angles in the circles shown below: <ABC intercepts minor arc AC <DEF intercepts major arc DGF *intercept means “forms”

  3. Theorem 12-9: Inscribed Angle Theorem A • The measure of an inscribed angle is equal to half of its intercepted arcs. C B

  4. Examples Find m<ABC Find m<ABC and m<ABD

  5. Examples Find m<DEF and mAEC Find m<ABC

  6. 3 inscribed < corollaries (thm sheet)

  7. Theorem 12-10 The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. B B D D C C

  8. Ex: find the numbered angles. 1 108˚ 32˚ 1 2 1 2 102˚ 1 61˚ 46˚

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