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Understanding Inscribed Angles in Geometry

Learn about inscribed angles, their properties, and how they relate to circles in geometry. Discover theorems and corollaries to understand the measures of inscribed angles and related arcs. Explore examples to solidify your knowledge.

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Understanding Inscribed Angles in Geometry

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  1. 10.4 Inscribed Angles

  2. Inscribed Angle • An angle with vertex on a circle and sides that contain chords of the circle.

  3. Thrm • The measure of an inscribed angle is ½ the measure of the intercepted arc. 102

  4. Corallary • If two inscribed angles intercept the same arc, then the angles are congruent. EX 80

  5. Corallary • If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

  6. Corallary • An angle inscribed in a semicircle is a right angle. Also, if an inscribed angle is right its intercepted arc is a semicircle. 90

  7. Thrm • The measure of a tangent-chord angle is ½ the measure of its intercepted arc. 220 110

  8. Examples 112

  9. Examples (cont) B A C D

  10. Home Work

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