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10.3 Inscribed Angles Objectives: (1) The student will be able to use inscribed angles to solve problems. (2) The student will be able to use properties of inscribed polygons. Toolbox: Summary: Inscribed Angle – an angle whose vertex is on a circle and whose sides contain chords of the circle. Intercepted Arc – arc that lies in the interior of an inscribed angle and has endpoints on the angle. Measure of an Inscribed Angle Theorem: If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc. m<ADB = ½ mAB Theorem: If two inscribed angles of a circle intercept the same arc, then the angles are congruent. Inscribed Polygon – if all the vertices of a polygon lie on a circle Circumscribed – the circle if the polygon is inscribed in it Theorems about Inscribed Polygons: ~ If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. ~ A quadrilateral can be inscribed in a circle its opposite angles are supplementary. Examples: ~ see extra examples on overheads Q: Explain why the diagonals of a rectangle inscribed in a circle are diameters of the circle. Hmwk: #9-29, 35, 42, & 43