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11.4 Inscribed Angles

Learn about the definitions, theorems, and examples related to inscribed angles in geometry, including the Inscribed Angle Theorem and its corollary. Explore how to find angle measures and intercept arc lengths.

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11.4 Inscribed Angles

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  1. 11.4 Inscribed Angles Geometry

  2. Definitions: • Inscribed Angle- Angle whose vertex is on a circle and whose sides contain chords of the circle. • Intercepted Arc- consists of endpoints that lie on the sides of an inscribed angle and all of the points of the circle between them. • Subtends- A segment or arc subtends an angle if endpoints lie on the sides of the angle

  3. Diagram:

  4. Inscribed Angle Theorem

  5. Examples: • Find each measure. • mPRU • mSP

  6. Example: • Find each measure. • mDAE

  7. Corollary (Easily proven theorem)

  8. Examples: • Find mEDF.

  9. Example: • Find mLJM.

  10. Example: • Find mABD and mBC in the string art.

  11. Theorem

  12. Example: • Find a.

  13. Example: • Find z.

  14. Example: • Find each measurement. • RUS • a

  15. Theorem

  16. Example: • Find the angle measures of GHJK.

  17. Example: • Find the angle measures of JKLM.

  18. Example: • Find the angle measures of ABCD.

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