Inscribed Angles

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!Chapter 9-4!
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Inscribed Angles
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What Youll Learn!

• To recognize and find measures of inscribed
  angles.
• To apply properties of inscribed figures.

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Why its Important!

• You can use inscribed angles to solve problems
  involving civil engineering and carpentry

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DeFiNiTiOnS

• Inscribed Angle An inscribed angle is an
  angle whose vertices is on the circle and whose
  sides each contain chords of the circle.
• Intercepted ArcThe arc of a circle within an
  inscribed angle.

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Theorem 9-4

• If an angle is inscribed in a circle, then the
  measure of the angle equals one-half the measure
  of its intercepted are.

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Example 1

• In the circle at the right, mST 68. Find mlt1
  and mlt2.

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Theorem 9-5

• If two inscribed angles of a circle or congruent
  circles intercept congruent arcs or the same arc,
  then the angles are congruent.

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Theorem 9-6

• If and inscribed angle of a circle intercepts a
  semicircle, then the angle is a right angle

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Example 2

• In A, mlt16x11, mlt29x19,mlt34y-25,
  mlt43y-9, and PQ RS. Find mlt1, mlt2, mlt3 and mlt4.
  

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Example 3

• Quadrilateral QRST is inscribed in C. if mltS
  28 and mltR110, find mltQ and mltT

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Theorem 9-7

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

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ThEEnD