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LESSON 11.3 INSCRIBED ANGLES

LESSON 11.3 INSCRIBED ANGLES. OBJECTIVE: To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord. CR.  A intercepts what arc? _____ m  O = ____ mCR = ____ m  A = ____. 60 °. 60 °. 30 °. INTERCEPTED ARC.

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LESSON 11.3 INSCRIBED ANGLES

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  1. LESSON 11.3 INSCRIBED ANGLES OBJECTIVE: To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord

  2. CR A intercepts what arc? _____ mO = ____ mCR = ____ mA = ____ 60° 60° 30° INTERCEPTED ARC THEOREM 11-9: The measure of an inscribed angle equals the measure of its HALF INTERCEPTED ARC

  3. QP QP A intercepts what arc? _____ B intercepts what arc? _____ mA = ____ mB = ____ 68° 68° Corollary 1: Angles inscribed in the same arc are CONGRUENT

  4. CDE CDE A intercepts what arc? ______ B intercepts what arc? ______ CDE is a ___________ mA = ____ mB = ____ SEMI-CIRCLE 90° 90° Corollary 2: Every angle inscribed in a semicircle is a RIGHT ANGLE

  5. mA = _____ mB = _____ mC = _____ mD = _____ 108° 90° 72° 90° Corollary 3: The opposite angles of a quadrilateral inscribed in a circle are SUPPLEMENTARY

  6. B A D C mA = mBC = mBCD = 120° 120° 60° THEOREM 11-10: The measure of an angle formed by a tangent and a chord is half the measure of its INTERCEPTED ARC

  7. Ex. #1 Find the value of a and b. 60 = ½ a P a 120°= a 60 T Q 30 b = ½ (a + 30) b S b = ½ (120 + 30) R b = ½ (150) An inscribed  is ½ the m of its int. arc. b = 75°

  8. Ex. #2 Find m1. m1 is 90°. 40° 70° 1 ’s inscribed in a semicircle = 90°.

  9. Ex. #3 Find m2. 70° 2 and 38° intercept same arc. 2 38° m2 = 38°. Angles that intcpt the same arc are .

  10. Ex. #4 Find the value of mLJK and y. mLJK = ½ JL J Q ½ JL= mQ = 35° 35 y mLJK = 35° L K s formed by tan.& chord = ½ the intcpt arc.

  11. mQJL = 180° mQJ = 180 - mJL mQJ = 180 - 70 mQJ = 110 y = ½mQJ Ex. #4 Find y. J Q 35 y L K y = 55° An inscribed  is ½ the m of its int. arc.

  12. ASSIGNMENT: Page 601 #1-3, 5-21 write the theorems for 5-21

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