Presentation on theme: "Arcs and Chords Warm Up Lesson Presentation Lesson Quiz"— Presentation transcript:
1 Arcs and Chords Warm Up Lesson Presentation Lesson Quiz Holt McDougal GeometryHolt Geometry
2 Warm Up1. What percent of 60 is 18?2. What number is 44% of 6?3. Find mWVX.302.64104.4
3 ObjectivesApply properties of arcs.Apply properties of chords.
4 Vocabulary central angle semicircle arc adjacent arcs minor arc congruent arcsmajor arc
5 A central angle is an angle whose vertex is the center of a circle 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.
7 Writing MathMinor arcs may be named by two points. Major arcs and semicircles must be named by three points.
8 Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.mKLF = 360° – mKJFmKJF = 0.35(360)= 126mKLF = 360° – 126°= 234
9 Check It Out! Example 1Use the graph to find each of the following.a. mFMCmFMC = 0.30(360)= 108Central is 30% of the .b. mAHB= 360° – mAMBc. mEMD= 0.10(360)mAHB= 360° – 0.25(360)= 36= 270Central is 10% of the .
10 Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.
11 Example 2: Using the Arc Addition Postulate Find mBD.mBC = 97.4Vert. s Thm.mCFD = 180 – (97.4 + 52)= 30.6∆ Sum Thm.mCD = 30.6mCFD = 30.6mBD = mBC + mCDArc Add. Post.= 97.4 Substitute.Simplify.= 128
12 Check It Out! Example 2aFind each measure.mJKLmKPL = 180° – ( )°mKL = 115°mJKL = mJK + mKLArc Add. Post.= 25° + 115°Substitute.= 140°Simplify.
13 Check It Out! Example 2bFind each measure.mLJNmLJN = 360° – ( )°= 295°
14 Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST UV.
16 Example 3A: Applying Congruent Angles, Arcs, and Chords TV WS. Find mWS.TV WS chords have arcs.mTV = mWSDef. of arcs9n – 11 = 7n + 11Substitute the given measures.2n = 22Subtract 7n and add 11 to both sides.n = 11Divide both sides by 2.mWS = 7(11) + 11Substitute 11 for n.= 88°Simplify.
17 Example 3B: Applying Congruent Angles, Arcs, and Chords C J, and mGCD mNJM. Find NM.GCD NJMGD NM arcs have chords.GD NMGD = NMDef. of chords
18 Example 3B ContinuedC J, and mGCD mNJM. Find NM.14t – 26 = 5t + 1Substitute the given measures.9t = 27Subtract 5t and add 26 to both sides.t = 3Divide both sides by 9.NM = 5(3) + 1Substitute 3 for t.= 16Simplify.
19 Check It Out! Example 3aPT bisects RPS. Find RT.RPT SPTmRT mTSRT = TS6x = 20 – 4x10x = 20Add 4x to both sides.x = 2Divide both sides by 10.RT = 6(2)Substitute 2 for x.RT = 12Simplify.
20 Check It Out! Example 3bFind each measure.A B, and CD EF. Find mCD.mCD = mEF chords have arcs.Substitute.25y = (30y – 20)Subtract 25y from both sides. Add 20 to both sides.20 = 5y4 = yDivide both sides by 5.CD = 25(4)Substitute 4 for y.mCD = 100Simplify.
22 Example 4: Using Radii and Chords Find NP.Step 1 Draw radius RN.RN = 17Radii of a are .Step 2 Use the Pythagorean Theorem.SN2 + RS2 = RN2SN = 172Substitute 8 for RS and 17 for RN.SN2 = 225Subtract 82 from both sides.SN = 15Take the square root of both sides.Step 3 Find NP.NP = 2(15) = 30RM NP , so RM bisects NP.
23 Check It Out! Example 4Find QR to the nearest tenth.Step 1 Draw radius PQ.PQ = 20Radii of a are .Step 2 Use the Pythagorean Theorem.TQ2 + PT2 = PQ2TQ = 202Substitute 10 for PT and 20 for PQ.TQ2 = 300Subtract 102 from both sides.TQ 17.3Take the square root of both sides.Step 3 Find QR.QR = 2(17.3) = 34.6PS QR , so PS bisects QR.
24 Lesson Quiz: Part I1. The circle graph shows the types of cuisine available in a city. Find mTRQ.158.4
25 Lesson Quiz: Part IIFind each measure.2. NGH1393. HL21
26 Lesson Quiz: Part III4. T U, and AC = Find PL to the nearest tenth. 12.9