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Exploring Inscribed Angles in Circle Geometry

Dive into the world of inscribed angles and polygons within circles, learning about the properties of intercepted arcs and angle congruency. Discover how to find angle measures and solve problems via an inscribed right triangle approach. This chapter covers key theorems and exercises for a comprehensive understanding of circle geometry concepts.

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Exploring Inscribed Angles in Circle Geometry

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  1. Chapter 10: Circles 10.4.1 Use Inscribed Angles and Polygons

  2. Inscribed Angles • An Inscribed Angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. • An Intercepted Arc is an arc whose endpoints are on an Inscribed Angle mDAB = ½ mDB 2*mDAB = mDB A D B

  3. Inscribed angle congruency Theorem • If two inscribed angles intercept the same arc, then the angles are congruent D A DAE  DBE B E

  4. Find the measure of each angle AE and BD are diameters mACD = mAED = A mBDE = mBED = B D C E

  5. What do you notice about BED and BD in the previous problem? • a right triangle is inscribed in a triangle iff the hypotenuse is a diameter B D F G E

  6. Homework • p. 676 • 1, 2, 5 – 8, 10 – 12, 16 – 18, 43 – 47odd

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