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GEOMETRY: Chapter 10 10.2: Arcs and Chords A central angle of a circle is an angle whose vertex is the center of the circle. In the diagram, angle ACB is the central angle of circle C. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 659. Use the diagram from last slide: If m A C B is less than 180 , then the points on o C that lie in the interior of m A C B form a m ino r arc w ith endpoints A and B . T he points on C that do not lie on m inor arc A B form a m ajor arc w ith endp oints A and B . A sem icircle is an arc w ith endpoints that are the en dpoints of a diam eter. N am ing A rcs: m inor arcs are nam ed by end points. M ajor arcs are nam ed by endpoints and on e point in betw een the endpoints such as A D B . Measuring Arcs: The measure of a minor arc is the measure of its central angle. T h e ex p ressio n m A B is read as "th e m easu re o f arc A B ." The measure of the entire circle is 360o. The measure of a major arc is the difference between 360o and the measure of the related minor arc. The measure of a semicircle is 180o. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 659. Ex.1: Find the m easure of each arc of C, w here A B is a diam eter. a. D B b. D A B c. A D B Answer: a. 135o; b. 225o ; c.180o Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 660. Postulate 23: Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 660. Ex. 2: A result of a survey about the ages of people in a town are shown. Find the indicated arc measures. a .m R U b .m R ST c .m R V T d .mU ST Answer: a. 140o ; b. 130o ; c. 230o ; d. 270o Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 660. Congruent Circles and Arcs Two circles are congruent circles if they have the same radius. Two arcs are congruent arcs if they have the same measure and they are arcs of the same circle or of congruent circles. If C is congruent to D , then you can w rite C D. Ex. 3: T ell w hether arcs C D and E F are congruent. E xplain w hy or w hy not. Images taken from: Geometry. McDougal Littell: Boston, 2007. P.661. Ex. 3: T ell w hether arcs C D and E F are congruent. E xplain w hy or w hy not. Images taken from: Geometry. McDougal Littell: Boston, 2007. P.661. 10.2, p. 607