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12-2

12-2. Arcs and Chords. Holt McDougal Geometry. Holt Geometry. Learning Targets. I will apply properties of arcs and chords. Vocabulary. central angle semicircle arc adjacent arcs minor arc congruent arcs major arc.

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12-2

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  1. 12-2 Arcs and Chords Holt McDougal Geometry Holt Geometry

  2. Learning Targets I will apply properties of arcs and chords.

  3. Vocabulary central angle semicircle arc adjacent arcs minor arc congruent arcs major arc

  4. A central angleis an angle whose vertex is the center of a circle. An arcis an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.

  5. Writing Math Minor arcs are named by the two endpoints of the arc. Major arcs and semicircles must be named by three points, with the endpoints being the first and third points named.

  6. mKLF = 360° – mKJF mKLF = 360° – 126° Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF. mKJF = 0.35(360) = 126 = 234

  7. b. mAHB Check It Out! Example 1 Use the graph to find each of the following. a. mFMC mFMC = 0.30(360) = 108 Central is 30% of the . = 360° – mAMB = 0.10(360) c. mEMD mAHB =360° –0.25(360) = 36 = 270 Central is 10% of the .

  8. Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.

  9. Find mBD. mBC = 97.4 mCD = 30.6 mBD = mBC + mCD Example 2: Using the Arc Addition Postulate Vert. s Thm. mCFD = 180 – (97.4 + 52) = 30.6 ∆Sum Thm. mCFD = 30.6 Arc Add. Post. = 97.4 + 30.6 Substitute. Simplify. = 128

  10. mJNL Check It Out! Example 2a Find each measure. 180° + 40° = 220°

  11. mLJN mLJN = 360° – (40 + 25)° Check It Out! Example 2b Find each measure. = 295°

  12. Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure STUV.

  13. TV WS. Find mWS. TV  WS mTV = mWS mWS = 7(11) + 11 Example 3A: Applying Congruent Angles, Arcs, and Chords  chords have arcs. Def. of arcs 9n – 11 = 7n + 11 Substitute the given measures. 2n = 22 Subtract 7n and add 11 to both sides. n = 11 Divide both sides by 2. Substitute 11 for n. = 88° Simplify.

  14. GD  NM GD NM Example 3B: Applying Congruent Angles, Arcs, and Chords C  J, andmGCD  mNJM. Find NM. GCD NJM  arcs have chords. GD = NM Def. of chords

  15. Example 3B Continued C  J, andmGCD  mNJM. Find NM. 14t – 26 = 5t + 1 9t = 27 t = 3 NM = 5(3) + 1 = 16

  16. PT bisects RPS. Find RT. mRT  mTS Check It Out! Example 3a RPT  SPT RT = TS 6x = 20 – 4x 10x = 20 x = 2 RT = 6(2) RT = 12

  17. mCD = mEF mCD = 100 Check It Out! Example 3b Find each measure. A B, and CD EF. Find mCD. 25y = (30y – 20) 20 = 5y 4 = y CD = 25(4)

  18. Step 1 Draw radius RN. Example 4: Using Radii and Chords Find NP. RN = 17 Step 2 Use the Pythagorean Theorem. SN2 + RS2 = RN2 SN2 + 82 = 172 SN2 = 225 SN= 15 Step 3 Find NP. NP= 2(15) = 30

  19. HOMEWORK: Pg 806, #5 – 18.

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