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6.4 Use Inscribed Angles and Polygons 6.3-6.4 Quiz: Friday Vocabulary • An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle. 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. Vocabulary • Measure of an Inscribed Angle Theorem – the measure of an inscribed angle is one half the measure of its intercepted arc. A 100o B 50o C Vocabulary • Theorem 6.10 – If two inscribed angles of a circle intercept the same arc, then the angles are congruent. 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. Vocabulary • Theorem 6.11 – If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. 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 180o) 90O 90O Example: • Find the indicated measure in circle P. a) angle S b) arc RQ You Try: Example: • Find the value of each variable. You Try: • Find the values of a and b. Classwork/Homework • P. 207 #1 – 18