11-3 Inscribed Angles - Yola

11-3 Inscribed Angles - Yola

11-3 Inscribed Angles Theorems: Inscribed Angle Theorem, 11-10 Corollaries: Corollaries to the Inscribed Angle Theorem Vocabulary: Inscribed angle, Intercepted arc Vocabulary A Intercepted Arc Inscribed Angle C B

AB is the intercepted arc of C C is an inscribed angle Theorem 11-9 (Inscribed Angle Theorem) The measure of an inscribed angle is half the measure of its intercepted arc. A 1 mB mAC 2 B C #1 Using the Inscribed Angle Theorem

Find mPQR if mRS 60 P 1 mTQR 90 2 mTQR 45 mPQR 45 60 mPQR 105 Q ao 60o T 30o

S bo R 60o Corollaries to the Inscribed Angle Theorem 1. 2. 3. Two inscribed angles that intercept the same arc are congruent. An angle inscribed in a semicircle is a right angle. The opposite angles of a quadrilateral inscribed in a circle are supplementary.

#2 Using Corollaries to Find Angle Theorem Find the diagram at the right, find the measure of each numbered angle. m1 90 1 m4 140 70 2 m3 90 1 m2 220 110 2 120o 1

60o 2 4 80o 100o 3 Theorem 11-10 The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. 1 mC mBDC 2 B B

D D C C #3 Using Theorem 11-10 Find x and y. J y 180 125 y 55 1 mx JL 2 1 mJQL JL

2 mx mJQL mQJL 90 90o Q 35o yo 55 xoo L K x 35

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