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Section 10.2: Angles and Arcs 1. I can define and identify major arcs, minor arcs, semicircles, and central angles and find their measures. 2. I can determine arc length of a circle. Angles and Arcs Central angle - an angle that intersects a circle in two points and has its vertex at the center. The sides of the central angle contain two radii of the circle. • The sum of the measures of the central angles of a circle is 360 degrees. A B • A central angle separates the circle into parts, each of which is an arc. • Arc - a part or portion of a circle that is defined by two endpoints. c Arcs Arcs are usually denoted by this symbol_______. Arcs of a Circle: Graphic Organizer Type of Arc: A minor arc - an arc with a measure of less than 180 degrees. C P A Major Arc Semicircle D J E C 60 110 M G B central angle B major arc - an arc with a measure of more than 180 degrees. Minor Arc Example: The measure of each arc is related to the measure of its central angle. Arc Degree Measure Equals By the letters of the two endpoints and another point on the arc. Ex: Usually by the letters of the two endpoints. Ex: By the letters of the two endpoints and another point on the arc. Ex: The measure of the 360 minus the measure 360 ÷2 or 180 degrees central angle. Less of the minor arc. than 180 degrees. Greater than 180 degrees. Congruent Arcs A Theorem 10.1: In the same or in congruent circles, two arcs are congruent if and only if their corresponding angles are congruent. But I forget how to determine if two circles are congruent? Review Examples: Finding the Measures of Central Angles & Arcs K L F Named: N D B 45 45 C Class, help Georgie out! 60 60 Are these arcs congruent? Find the measure of the following Central Angles & Arcs : D O A 45 E 20 C B a. Angle AOD ______________ b. Arc AD _________________ c. Angle DOC _______________ d. Angle AOB _______________ e. Arc ADE _________________ 1 Examples: Finding the Measures of Arcs Arc Addition Postulate: Arcs of a circle that have exactly one point in common are adjacent arcs. The measure of adjacent arcs can be added. C A O Find the measure of each arc: B Postulate 10.1: C A Arc AB ____________ Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs. __________________________ 40 E Arc ABD ___________ 80 110 B Arc AD _____________ D Arc Length Examples: Using Proportions to Find Arc Length A • Another way to measure an arc is by its length. arc length - The distance along the curved line making up the arc. D C • An arc is part of the circle which means its length is part of the circumference of the circle. 15 Find the length of each arc for the given angle measure. H 120 B G C E a. Arc DE if m DCE = 100 Link to Interactive • To find arc length I can use a proportion or a formula. degree measure of arc degree measure of whole circle A = 360 l 2 πr arc length circumference ______________________________ F A = l b. Arc HDF if m HCF = 125 360 2πr ______________________________ • Expressed as a formula AxC=l 360 A = degree measure of arc C = circumference l = arc length AxC=l 360 Use the formula this time. C. Arc HD if m DCH = 45 ______________________________ 2

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