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12-2 12-2 Arcs Arcsand andChords Chords Warm Up Lesson Presentation Lesson Quiz HoltMcDougal GeometryGeometry Holt 12-2 Arcs and Chords Warm Up 1. What percent of 60 is 18? 30 2. What number is 44% of 6? 2.64 3. Find mWVX. 104.4 Holt McDougal Geometry 12-2 Arcs and Chords Objectives Apply properties of arcs. Apply properties of chords. Holt McDougal Geometry 12-2 Arcs and Chords Vocabulary central angle arc minor arc major arc Holt McDougal Geometry semicircle adjacent arcs congruent arcs 12-2 Arcs and Chords A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. Holt McDougal Geometry 12-2 Arcs and Chords Holt McDougal Geometry 12-2 Arcs and Chords Writing Math Minor arcs may be named by two points. Major arcs and semicircles must be named by three points. Holt McDougal Geometry 12-2 Arcs and Chords Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF. mKLF = 360° – mKJF mKJF = 0.35(360) = 126 mKLF = 360° – 126° = 234 Holt McDougal Geometry 12-2 Arcs and Chords Check It Out! Example 1 Use the graph to find each of the following. a. mFMC mFMC = 0.30(360) = 108 Central is 30% of the . b. mAHB = 360° – mAMB c. mEMD = 0.10(360) mAHB = 360° – 0.25(360) = 36 = 270 Holt McDougal Geometry Central is 10% of the . 12-2 Arcs and Chords Example 2: Using the Arc Addition Postulate Find mBD. mBC = 97.4 mCFD = 180 – (97.4 + 52) = 30.6 mCD = 30.6 mBD = mBC + mCD = 97.4 + 30.6 = 128 Holt McDougal Geometry 12-2 Arcs and Chords Check It Out! Example 2a Find each measure. mJKL mKPL = 180° – (40 + 25)° mKL = 115° mJKL = mJK + mKL = 25° + 115° = 140° Holt McDougal Geometry 12-2 Arcs and Chords Check It Out! Example 2b Find each measure. mLJN mLJN = 360° – (40 + 25)° = 295° Holt McDougal Geometry 12-2 Arcs and Chords In circles, or in congruent circles: Congruent central angles Congruent chords Congruent arcs Holt McDougal Geometry 12-2 Arcs and Chords Example 3A: Applying Congruent Angles, Arcs, and Chords TV WS. Find mWS. TV WS mTV = mWS 9n – 11 = 7n + 11 2n = 22 n = 11 mWS = 7(11) + 11 = 88° Holt McDougal Geometry 12-2 Arcs and Chords Example 3B: Applying Congruent Angles, Arcs, and Chords C J, and mGCD mNJM. Find NM. GD NM GCD NJM GD NM arcs have chords. GD = NM Holt McDougal Geometry 12-2 Arcs and Chords Example 3B Continued C J, and mGCD mNJM. Find NM. 14t – 26 = 5t + 1 9t = 27 t=3 NM = 5(3) + 1 = 16 Holt McDougal Geometry 12-2 Arcs and Chords Check It Out! Example 3a PT bisects RPS. Find RT. RPT SPT mRT mTS RT = TS 6x = 20 – 4x 10x = 20 x=2 Add 4x to both sides. Divide both sides by 10. RT = 6(2) Substitute 2 for x. RT = 12 Simplify. Holt McDougal Geometry 12-2 Arcs and Chords Check It Out! Example 3b Find each measure. A B, and CD EF. Find mCD. mCD = mEF 25y = (30y – 20) 20 = 5y 4=y CD = 25(4) mCD = 100 Holt McDougal Geometry 12-2 Arcs and Chords Holt McDougal Geometry 12-2 Arcs and Chords Example 4: Using Radii and Chords Find NP. Step 1 Draw radius RN. RN = 17 Radii of a are . Step 2 Use the Pythagorean Theorem. SN2 + RS2 = RN2 SN2 + 82 = 172 SN2 = 225 SN = 15 Substitute 8 for RS and 17 for RN. Subtract 82 from both sides. Take the square root of both sides. Step 3 Find NP. NP = 2(15) = 30 Holt McDougal Geometry RM NP , so RM bisects NP. 12-2 Arcs and Chords Check It Out! Example 4 Find QR to the nearest tenth. Step 1 Draw radius PQ. PQ = 20 Radii of a are . Step 2 Use the Pythagorean Theorem. TQ2 + PT2 = PQ2 Substitute 10 for PT and 20 for PQ. TQ2 + 102 = 202 Subtract 102 from both sides. TQ2 = 300 TQ 17.3 Take the square root of both sides. Step 3 Find QR. QR = 2(17.3) = 34.6 Holt McDougal Geometry PS QR , so PS bisects QR. 12-2 Arcs and Chords Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find mTRQ. 158.4 Holt McDougal Geometry 12-2 Arcs and Chords Lesson Quiz: Part II Find each measure. 2. NGH 3. HL 139 21 Holt McDougal Geometry 12-2 Arcs and Chords Lesson Quiz: Part III 4. T U, and AC = 47.2. Find PL to the nearest tenth. 12.9 Holt McDougal Geometry