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6.4 Use Inscribed Angles and Polygons 6.3-6.4 Quiz: Friday
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Vocabulary An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.
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Vocabulary The arc that lies in the interior of an inscribed angles and has endpoints on the angle is called the intercepted arc of the angle.
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Vocabulary Measure of an Inscribed Angle Theorem –the measure of an inscribed angle is one half the measure of its intercepted arc. 50 o A B C 100 o
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Vocabulary Theorem 6.10 –If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
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Vocabulary A polygon is an inscribed polygon if all of its vertices lie on a circle. The circle that contains the vertices is a circumscribed circle. –Remember: a polygon is a closed figure made up of 3 or more straight lines.
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Vocabulary Theorem 6.11 –If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.
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Vocabulary Theorem 6.12 –A quadrilateral (4-sided figure) can be inscribed in a circle if and only if its opposite angles are supplementary (add up to be 180 o ) 90 O
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Example: Find the indicated measure in circle P. a) angle Sb) arc RQ
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You Try:
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Example: Find the value of each variable.
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You Try: Find the values of a and b.
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Classwork/Homework P. 207 #1 – 18
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