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Understanding Angles by Secants and Tangents in Circles

Learn how to define angles created by secants and tangents in circles, apply theorems on arc measures, and solve angle classifications in different cases. Practice problems provided for independent work.

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Understanding Angles by Secants and Tangents in Circles

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  1. Angles Formed by Secants and Tangents Section 9.4 Pg. 588 Mrs. Riggle

  2. Lesson Objectives • Today we will learn how to: • Define angles formed by secants and tangents of circles. • Use theorems about measures of arcs intercepted by these angles.

  3. Classifications of Angles with Circles

  4. Case 1: Vertex On Circle • Find each measure: • m<BCD • mABC

  5. Case 2: Vertex Inside Circle • Find the angle measure: • m<SQR

  6. Case 3: Vertex Outside Circle • Find the value of x:

  7. Summary

  8. You try! Remember -Vertex On Circle = ½ measure of the arc. -Vertex Inside Circle = ½ sum of the intercepted arcs. -Vertex Outside Circle = ½ difference of the intercepted arcs.

  9. Independent Work Pgs. 593–594, #11–25, odds. Check your answers in the back of the textbook when you are finished. Work to be Submitted 9.4 EdMastery Assignment Due 4p.m. Friday, April 15, 2011. Assignment Have a nice weekend!

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