Sim (brhs)

Sim (brhs)

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  Hilda D. Dragon
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  LEAST MASTERED SKILLS: InscribedAngles and Intercepted Arcs SUB TASKS: 1. Identify inscribed angles and their intercepted arcs 2. Apply the key concept of inscribed angles and intercepted arc 3. Solve real-life problems involving inscribed angles and intercepted arcs
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  What is anInscribed Angle? Inscribed Angle is an angle whose vertex is on a circle and whose sides contain chords of a circle. What is an Intercepted Arc? It is an arc that lies in the interior of an inscribed angle and has endpoints on the angle.
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  I If an angleis inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc. C To check, m∟ABC=½ mAC =½ (86 ̊) =43 ̊ A B 86 ̊43 ̊ ͡
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  If two inscribedangles of a circle intercept congruent arcs or the same arc, then the angles are congruent. C D In the figure ∟CAD and ∟CBD intercept CD. Therefore, m∟CAD=m∟CBD. If m∟CAD=45 ̊then m∟CBD=45 ̊. ͡
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  If an inscribedangle of a circle intercepts a semicircle, then the angle is a right angle. Then m∟ABC=90 ̊. Let’s try apply it to find x ̊. The triangle angle sum theorem explains that…………. m∟A +m∟B +m∟C = 180 ̊ Substituting the value, 50 ̊+ 90 ̊ + x ̊ = 180 ̊ 140 ̊ + x ̊ = 180 ̊ x ̊= 180 ̊-140 ̊ x ̊ = 40 ̊
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  If a quadrilateralis inscribed in a circle, then its opposite angles are supplementary. Using the figure, to find the m∟F it will be: m∟D = m∟F 85 ̊= m∟F
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  Activity 1. FindMe! 1.Name all the inscribed angles in the figure. 2. Which inscribed angles intercept the following arcs? a. AB b. CD C D Very Good! Try the next one  ͡ ͡
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  Activity 2. Let’sPractice! 1.Given Circle with circle indicated. Find x. Choose: ____ 36 ____ 54 ____ 90 ____ 108
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  2. Given thediameter. Find x. Choose: _____ 45 _____ 60 _____ 90 _____ 180
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  3. Given thediameter. Find x. Choose: ____ 28 ____ 56 ____ 62 ____ 124
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  Activity 3. MeasureMe! 1.If m∟A = 45 ̊, find: a. m∟B, why? b. mCD, why? 2. If m AB = 30 ̊, find: a. m∟1, why? b. m∟2, why? ͡ 1 2 ͡ C D Wow, good job……try the next 
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  Y You can do this Activity 4. Half, Equalor Twice As? 1. Which inscribed angles are congruent? Why? 2. If m∟CBD=54, what is the measure of CD? 3. If m∟ABD=5x+3 and m∟DCA=4x+10, find a. the value of x c. m∟DCA b. m∟ABD d. mAD 4. If m∟BDC=6x-4 and mBC=10x+2, find: a. the value of x c.mBC b. m∟BDC d. m∟BAC E D C B A ͡ ͡ ͡ ͡ Very good! Now you’re ready 
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  I believe I cando this… Direction: Use the given figures to answer the following. 1. CAR is inscribed in circle E. If m∟C=80 and mRC= 150, find: a. mAR b. mAC c. m∟A d. m∟R 2. HD is a diameter of circle O. If mRD = 70 ̊, find: a. m∟H c. m∟R b. m∟D d. mRH e. mHD .E C A R ͡ ͡ ͡ ͞ .O R D H ͡ ͡
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  3. Quadrilateral HOPEis inscribed in circle S. If m∟HOP = 80 and m∟OPE=75, find: a. m∟PEH b. m∟EHO 4. Isosceles YOUis inscribed in circle R.IfmUO=120 ̊, find: a. m∟YOU b. m∟YOU c. mYU d. mYO H .S E P O ͡ Y O U .R ͡ ͡ Well done…Good job!!!
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  Activity : TakeMe To Your RealWorld! Answer the following questions. 1. What kind of parallelogram can be inscribed in a circle? Explain. 2. There are circular garden having paths in the shape of an inscribed square like one shown below. a. Determine the measure of an arc intercepted by an inscribed angle formed by the square in the garden. b. What is the measure of an inscribed angle in a garden in a garden with a square? Explain.
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  Learner’s Module ,First Edition 2015 pp. 165-175 Callanta, Melvin. et al. Geometry, Third Year pp. 205-207 Bernabe, Julieta. et al http://www.iq.poquoson.org/math.htm http://www.math-worksheets.org/inscribed -angles http://www.onlinemathlearning.com/circle-theorems.html