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P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters To name: use 3 letters <APB is a Central Angle
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P E F D Semicircle: An Arc that equals 180° EDF To name: use 3 letters EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of 180°
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THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs are Supplementary
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Vertical Angles are Equal
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Linear Pairs are Supplementary http://www.mathopenref.com/linearpair.html 120°60°
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measure of an arc = measure of central angle A B C Q 96 m AB m ACB m AE E = = = 96° 264° 84°
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Arc Addition Postulate A B C m ABC = m AB + m BC
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Tell me the measure of the following arcs. 80 100 40 140 A B C D R m DAB = m BCA = 240 260
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Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles. 45 A B C D 110
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Classwork Page 193 #9-18 You have 15 minutes.
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Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INSCRIBED ANGLE INTERCEPTED ARC
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Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. C L O T 1. YES; CL
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Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. Q R K V 2. NO; QVR S
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160° 80° To find the measure of an inscribed angle…
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http://www.geogebra.org /en/upload/files/english/ Guy/Circles_and_angles/ Inscribed_Anlge.html
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120 x What do we call this type of angle? What is the value of x? y What do we call this type of angle?How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!!
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http://www.geogebra.org/en/upload/fi les/english/Guy/Circles_and_angles/I nscribed_angle_practice.html
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Examples 3. If m JK = 80 , find m <JMK. M Q K S J 4. If m <MKS = 56 , find m MS. 40 112
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72 If two inscribed angles intercept the same arc, then they are congruent.
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http://www.geogebra.org/en/upload /files/english/Guy/Circles_and_ang les/Inscribed_angle_practice.html
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Example 5 In J, m< A= 5x and m< B = 2x + 9. Find the value of x. A Q D J T U B m<A = m<B 5x = 2x+9 x = 3
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Classwork: Page 193 #9-23 Page 207 #1-15
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Whatever is left is homework
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