Presentation on theme: "Arcs and Chords Warm Up Lesson Presentation Lesson Quiz"— Presentation transcript:
1Arcs and Chords Warm Up Lesson Presentation Lesson Quiz Holt McDougal GeometryHolt Geometry
2Warm Up1. What percent of 60 is 18?2. What number is 44% of 6?3. Find mWVX.302.64104.4
3ObjectivesApply properties of arcs.Apply properties of chords.
4Vocabulary central angle semicircle arc adjacent arcs minor arc congruent arcsmajor arc
5A 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.
7Writing MathMinor arcs may be named by two points. Major arcs and semicircles must be named by three points.
8Example 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
9Check 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 .
10Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.
11Example 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
12Check It Out! Example 2aFind each measure.mJKLmKPL = 180° – ( )°mKL = 115°mJKL = mJK + mKLArc Add. Post.= 25° + 115°Substitute.= 140°Simplify.
13Check It Out! Example 2bFind each measure.mLJNmLJN = 360° – ( )°= 295°
14Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST UV.
16Example 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.
17Example 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
18Example 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.
19Check 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.
20Check 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.
22Example 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.
23Check 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.
24Lesson Quiz: Part I1. The circle graph shows the types of cuisine available in a city. Find mTRQ.158.4
25Lesson Quiz: Part IIFind each measure.2. NGH1393. HL21
26Lesson Quiz: Part III4. T U, and AC = Find PL to the nearest tenth. 12.9