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Geometry 10.4 – Use Inscribed Angles and Polygons Learning Target: By the end of today’s lesson we will be able to successfully use inscribed angles of circles. Vocabulary Definition Illustrations An inscribed angle is an angle whose Inscribed Angle ____________ is on a circle and whose sides contain ________ of the circle. The arc that lies in the interior of an _______________ angle and has Intercepted Arc _______________ on the angle is called the intercepted arc of the angle. Inscribed Polygon A polygon is an inscribed polygon if all of its ______________ lie on a circle. A circumscribed circle is a circle that Circumscribed Circle contains the vertices of an ______________ polygon. MEASURE OF AN INSCRIBED ANGLE THEOREM The measure of an inscribed angle is one half the measure of its____________________________. mADB = ½ • _________ 1) Find the indicated measure in P. a) mS b) Measure of arc RQ. 2) Find the measure of arc HJ and HGJ. What do you notice about HGJ and HFJ? If two inscribed angles of a circle intercept the same arc, then the angles are _____________. ADB _________ 3) Name two pairs of congruent angles in the figure. 4) Find the indicated measure. a) mGHJ b) Measure of arc CD c) mRTS If a _________ triangle is inscribed in a circle, then the ____________is a diameter of the circle. Conversely, if one side of an inscribed triangle is a ________________ of the circle, then the triangle is a ___________ triangle and the angle opposite the diameter is the___________ angle. mABC = 90 if and only if ______ is a diameter of the circle. A quadrilateral can be inscribed in a circle if and only if its opposite angles are_______________. D, E, F, and G lie on C if and only if mD + mF = mE + mG = ________. 5) Find the value of each variable. a) b) c)

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