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GEOMETRY: Chapter 10

GEOMETRY: Chapter 10. 10.3: Inscribed Angles. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle.

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GEOMETRY: Chapter 10

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  1. GEOMETRY: Chapter 10 10.3: Inscribed Angles

  2. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 672.

  3. Theorem 10.8: Measure of an Inscribed Angle Theorem The measure of an inscribed angle is one half the measure of its intercepted arc. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 672.

  4. Theorem 10.9 If two inscribed angles of a circle intercept the same arc, then the angles are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 673.

  5. Ex.1: Answer: a. 50o; b. 1100 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 673.

  6. Ex. 2: Answer: 104 degrees, 52 degrees. The angles are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 673.

  7. Ex. 3: Answer: angle R is congruent to angle S, Angle U is congruent to angle T Images taken from: Geometry. McDougal Littell: Boston, 2007. P.674.

  8. Theorem 10.10: If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 674.

  9. Ex. 4:A graphic design software program was used in a home improvement store to design kitchen cabinets. The designer showed a wall of cabinets with a 90o viewing angle at P. From what other positions would the cabinets fill a 90o viewing window? Answer: from any position on a semicircle that has segment AB as a diameter Images taken from: Geometry. McDougal Littell: Boston, 2007. P.674.

  10. Theorem 10.11 A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 675.

  11. Ex. 5: Find the value of each variable. Answer: a. x = 80, y = 120; b. x =15, y = 5 Images taken from: Geometry. McDougal Littell: Boston, 2007. P.675.

  12. 10.3, p. 616, #3-23 all

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