Inscribed Angles

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Inscribed Angles

• 10.3

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Definitions
Inscribed angle- an angle whose vertex is on a
circle and whose sides contain chords of the
circle. Intercepted Arc- the arc that lies in
the interior of an inscribed angle and has
endpoints on the angle.
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Theorem 10.8

• If an angle is inscribed in a circle, then its
  measure is half the measure of its intercepted
  arc.

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Theorem 10.9
If two inscribed angles or a circle intercept the
same arc, then the angles are congruent.
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Definition

• Inscribed Polygon- a polygon with all vertices on
  the circle.
• Circumscribed Circle- a circle with an inscribed
  polygon.

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Theorem 10.10

• A right triangle is inscribed in a circle iff the
  hypotenuse is a diameter of the circle.

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Theorem 10.11

• A quadrilateral can be inscribed in a circle iff
  its opposite angles are supplementary.

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Homework

• Pg. 616
• 3,4,9,10,15,16,18,19,21,22
• Quiz over 10.1-10.3 Tomorrow
• (5 questions)