Pre-AP Geometry 12-2 Study Guide: Arcs and Chords (pp ) Page! 1 of! 12
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1 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 1 of! 12 ttendance Problems 1. What percent of 60 is 18? 2. What number is 44% of 6? 3. Find! m!wvx. I can apply properties of arcs. I can apply properties of chords. Vocabulary rc djacent rcs Semicircle Minor arc congruent arcs entral angle Major rc
2 GRPH Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 2 of! 12 ommon ore.9-12.g..2 Identify and describe relationships among inscribed angles, radii, and chords..12.2:.9-12.g.o.12 Make formal geometric constructions with a variety of tools and methods. central angle is an angle whose vertex is the center of a circle. n arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. Question: What is the hidden math term? nswer: ircle graph. "Transform adversity into an enjoyable challenge! uthor and Researcher, Mihalyi zikszent
3 2-2! rcs and hords s erties of arcs. erties of Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Identify and describe relationships among inscribed angles, radii, and chords..o.12 Who uses this? Market analysts use circle graphs to compare sales of different products. Page! 3 of! 12 ry le central angle is an angle whose vertex is the center of a circle. n arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. rcs arcs rcs and Their Measure R MSUR IGRM minor arc is an arc whose points are on or in the interior of a central angle. The measure of a minor arc is equal to the measure of its central angle. m = m = x x cs may d by two ajor arcs icircles must d by ints. major arc is an arc whose points are on or in the exterior of a central angle. Writing Math If the endpoints of an arc lie on a diameter, the arc is a semicircle. The measure of a major arc is equal to 360 minus the measure of its central angle. m = m = x The measure of a semicircle is equal to 180. Minor arcs may be named by two points. Major arcs and semicircles must be named by three points. m FG = 180 F x G XMPL 1 ata pplication The circle graph shows the types of music sold during one week at a music store. Find m. m = m M m M = 0.13 (360 ) = 46.8 m of arc = m of central. entral is 13% of the. Jazz 3% H G F lassical 3% Use the graph to find each of the following. 1a. m FM 1b. m H Music Sales Pop 9% Other 26% M ountry 10% Rock 25% 1c. m M Rap 13% R & 11% rand X Pictures/PunchStock apter 12 ircles 2L02.indd :23:48 PM
4 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 4 of! 12 xample 1. The circle graph shows the types of grass planted in the yards of one neighborhood. Find! mklf!. Guided Practice. Use the graph to find each of the following. 4.! m!fm 5.! mh! 6.! m!m
5 ! Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 5 of! 12 djacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs. djacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs. R S T Postulate rc ddition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. m = m + m MPL 2 Using the rc ddition Postulate Find m m = 90 m F = 90 m F = 18 m = 18 m = m + m = = 108 Find each measure. xample 2. Find 2a.! m! m. JKL Vert. Thm. m F = 18 rc dd. Post. Substitute and simplify. 2b. m LJN K J 18 L 40 M N P 25 F Within a circle or congruent circles, congruent arcs are Guided two arcs Practice. that have Find the each same measure. In the figure, ST UV. 7.! mjkl! 8.! mljn! U x x V S T Theorem THORM HYPOTHSIS ONLUSION In a circle or congruent circles: (1) ongruent central angles have congruent chords. (2) ongruent chords
6 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 6 of! 12 Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure! ST! UV!.
7 4. 4. PT Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 7 of! 12 MPL 3 pplying ongruent ngles, rcs, and hords Find each measure. RS TU. Find m RS. RS TU chords have arcs. m RS = m TU ef. of arcs 3x = 2x + 27 Substitute the given measures. x = 27 Subtract 2x from both sides. m RS = 3 (27) Substitute 27 for x. = 81 Simplify. R U 3x S T (2x + 27), and F. Find m F. F arcs have central. m = m F ef. of 5y + 5 = 7y - 43 Substitute the given measures. 5 = 2y - 43 Subtract 5y from both sides. 48 = 2y dd 43 to both sides. 24 = y ivide both sides by 2. m F = 7 (24) - 43 Substitute 24 for y. = 125 Simplify. (5y + 5) F (7y - 43) xample 3. Find each measure. Find.! TV WS. Find! mws! each measure.. 3a. PT bisects RPS. Find RT. P R 6x T 3b., and F. Find m. S 20-4x (30y - 20) F 25y er 12 ircles.indd 804 3/4/11 7:43:53
8 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 8 of! 12.! J, and! m!g m!njm. Find NM. Guided Practice. Find each measure.!!!" 9.! PT bisects!!rps. Find RT.
9 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 9 of! ! &! F. Find! m! rcs and chords: (p 807) 21, 23, 25, 27, 29, 30.
10 ! You will prove Theorems and in xercises 42 and 43 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) Page! 10 of! 12 MPL 4 Using Radii and hords Find. 2 Step 1 raw radius. 3 = 5 Radii of a are. Step 2 Use the Pythagorean Theorem = = = 16 = 4 Step 3 Find. = 2(4 ) = 8 Substitute 3 for and 5 for. Subtract 3 2 from both sides. Take the square root of both sides., so bisects. 4. Find QR to the nearest tenth. Q P T S R THINK N ISUSS 1. What is true about the measure of an arc whose central angle is obtuse? 2. Under what conditions are two arcs the same measure but not congruent? 3. GT ORGNIZ opy and complete the graphic organizer. In each box, write a definition and draw a sketch. djacent arcs Major arc rcs ongruent arcs Minor arc 12-2 rcs and hords 805
11 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) xample 4. Find NP. Page 11! of 12!
12 Pre-P Geometry 12-2 Study Guide: rcs and hords (pp ) 11. Guided Practice. Find QR. Round your final answer to the nearest tenth. Page! 12 of! rcs and chords: (p 807) 21, 23, 25, 27, 29-35, 37, 38, 40,
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