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This lesson explores the concept of inscribed angles in circles, including key theorems and their applications. Students will discover how to measure inscribed angles in relation to intercepted arcs, specifically focusing on the Inscribed Angle Theorem. The class will engage in practice problems to apply their understanding and analyze congruent angles. To reinforce learning, students will work in pairs and groups to solve exercises and a proof related to inscribed angles, enhancing collaborative problem-solving skills.
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Bellwork • If circle G has a radius of 6, what is the measure of GH? • Bonus: What is the measure of EH?
Homework Check • 18) 42 • 19) 6.71 • 21) 98.3 ft • 22) 8 • 7) 21 • 9) 127 • 11) 7 • 13) 27 • 15) 122.5
Inscribed Angles • Miss Pahls • 4/2/14
Inscribed Angles • Vertex on the circle • Sides are Chords across the circle
Intercepted Arc • The intercepted arc lies on the inside of an inscribed angle. • In this case: Arc SQ
Inscribed Angle Theorem • If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
With your partner: • Please find: • mCF • m∠C
Congruency Theorem • If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent.
