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Understanding Inscribed Angles and Their Relationships in Circle Geometry

Inscribed angles are fundamental concepts in circle geometry, defined as angles with their vertex on the circumference of the circle and sides that extend to chords within the circle. This resource explores the relationship between inscribed angles and their intercepted arcs, detailing that an inscribed angle measures half the intercepted arc's degree. We also cover critical theorems, such as the congruence of angles that intercept the same arc and the properties of angles intercepting a semicircle, providing exercises for practice.

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Understanding Inscribed Angles and Their Relationships in Circle Geometry

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  1. 8-3A Inscribed Angles What is an inscribed angle? What is the relationship between an inscribed angle and its intercepted arc?

  2. Find the measure of each arc 54° 180° 306° E • mDE • mAED • mEBD 54° A D C B What kind of angle is angle ECD? Central angle

  3. B C A Definition His name was inscribed on the award. The square is inscribed in the circle. An inscribed angle is an angle with its vertex on a circle and sides that contain chords of the circle.

  4. Sizing Up Inscribed Angles A • Measure the central angle • What is the measure of the arc AB? • Measure the inscribed angle • Compare the measure of the central angle and the inscribed angle. C B D

  5. Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc. A C B

  6. Find the measure of each angle or arc indicated by a variable. x° C 24° z° 160° 48° 90° y° 80°

  7. Theorem If two inscribed angles intercept the same arc, then they are congruent. A D B C

  8. Theorem An inscribed angle that intercepts a semicircle is a right angle.

  9. What is an inscribed angle? An inscribed angle is an angle with its vertex on a circle and sides that contain chords of the circle. • What is the relationship between an inscribed angle and its intercepted arc? The measure of an inscribed angle is half the measure of its intercepted arc.

  10. Assignment 8-3A Page 586, 1-6, 8-12, 29-36

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