Arcs, Central and Inscribed Angles ACTIVITY 4.2 continued Coming Full Circle SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Close Reading, Interactive Word Wall, Vocabulary Organizer ___ My Notes ___ 4. Below is a diagram of circle O. OA and OB are called ______. Q A O ACADEMIC VOCABULARY central angle B Points A and B divide the circle into two arcs. The smaller arc is known as the minor arc AB , and the larger arc is known as major arc AQB . The angle formed by the two radii, ∠AOB, is called a central angle of this circle. In general, a central angle is an angle whose vertex is at the center of a circle and whose sides contain radii of the circle. An arc intercepted by a central angle is the minor arc that lies in the interior of the angle. Notice that the major arc associated with points A and B lies outside ∠AOB, while the minor arc lies in the interior of ∠AOB. AB is said to be intercepted by ∠AOB. By definition, the measure of a minor arc is equal to the measure of the central angle that intercepts the minor arc. The notation for “the measure of AB ” is m AB . The notation for a minor arc requires the endpoints of the arc, AB . The notation for a major arc requires a point on the arc included between the endpoints of the arc, AQB . Semicircles are named as major arcs. • The measure of a minor arc must be between 0° and 180°. • The measure of a major arc must be at least 180° and less than 360°. © 2010 College Board. All rights reserved. The measure of a semicircle is 180°. Unit 4 • Circles and Constructions 287 ACTIVITY 4.2 Arcs, Central and Inscribed Angles continued Coming Full Circle SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Quickwrite My Notes TRY THESE A ___ __ Given the circle below with center C, diameters JR and KQ and m∠RCQ = 50°. Use the definitions for central angle and intercepted arc along with triangle properties to find each of the following. = _____° a. mRQ = ______° b. mJQ Q C J R c. m∠CRQ = _______° K = ______° d. mJQR = ______° e. mJKQ _______. Write a definition for congruent arcs. f. JK TRY THESE B __ ___ ___ Given the circle ___below with center C and diameters JR, KQ and PL. ___ __ PL ⊥ JR and KQ bisects ∠PCR. P C J b. m∠1 + m∠2 = ______° = m_____°. Explain. + mPQ c. mJP = ______° d. mJQ e. m∠JRQ = ______° = ______° f. mJL g. m∠JRL = ______°. Explain. 288 SpringBoard® Mathematics with MeaningTM Geometry K L 2 Q 1 R © 2010 College Board. All rights reserved. QR . a. Explain why PQ
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