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Geometry B Chapter 10

Geometry B Chapter 10. Arcs and Chords. Objectives. Apply properties of arcs and chords. Warm Up 1. What percent of 60 is 18? 2. What number is 44% of 6? 3. Find m WVX. 30. 2.64. 104.4. Vocabulary. central angle semicircle arc adjacent arcs minor arc congruent arcs

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Geometry B Chapter 10

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  1. Geometry BChapter 10 Arcs and Chords

  2. Objectives Apply properties of arcs and chords.

  3. Warm Up 1.What percent of 60 is 18? 2. What number is 44% of 6? 3. Find mWVX. 30 2.64 104.4

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

  5. 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.

  6. Writing Math Minor arcs may be named by two points. Major arcs & semicircles named by three points.

  7. 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

  8. b. mAHB In Your Notes! 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 .

  9. Adjacent arcsare arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs. Turn to page 706

  10. 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

  11. mJKL mKL = 115° mJKL = mJK + mKL In Your Notes! Example 2a Find each measure. mKPL = 180° – (40 + 25)° Arc Add. Post. = 25° + 115° Substitute. = 140° Simplify.

  12. mLJN mLJN = 360° – (40 + 25)° In Your Notes! Example 2b Find each measure. = 295°

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

  14. Turn to Page 707

  15. 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.

  16. 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

  17. Example 3B Continued C  J, andmGCD  mNJM. Find NM. 14t – 26 = 5t + 1 Substitute the given measures. 9t = 27 Subtract 5t and add 26 to both sides. t = 3 Divide both sides by 9. NM = 5(3) + 1 Substitute 3 for t. = 16 Simplify.

  18. PT bisects RPS. Find RT. mRT  mTS In Your Notes! Example 3a RPT  SPT RT = TS 6x = 20 – 4x 10x = 20 Add 4x to both sides. x = 2 Divide both sides by 10. RT = 6(2) Substitute 2 for x. RT = 12 Simplify.

  19. mCD = mEF mCD = 100 In Your Notes! Example 3b Find each measure. A B, and CD EF. Find mCD.  chords have arcs. Substitute. 25y = (30y – 20) Subtract 25y from both sides. Add 20 to both sides. 20 = 5y 4 = y Divide both sides by 5. CD = 25(4) Substitute 4 for y. Simplify.

  20. Turn to Page 716

  21. Step 1Draw radius RN. RM NP , so RM bisects NP. Example 4: Using Radii and Chords Find NP. RN = 17 Radii of a are . Step 2Use the Pythagorean Theorem. SN2 + RS2 = RN2 SN2 + 82 = 172 Substitute 8 for RS and 17 for RN. SN2 = 225 Subtract 82 from both sides. SN= 15 Take the square root of both sides. Step 3Find the length. NP= 2(15) = 30

  22. Step 1Draw radius PQ. PS QR , so PS bisects QR. In Your Notes! Example 4 Find QR to the nearest tenth. PQ = 20 Radii of a are . Step 2Use the Pythagorean Theorem. TQ2 + PT2 = PQ2 TQ2 + 102 = 202 Substitute 10 for PT and 20 for PQ. TQ2 = 300 Subtract 102from both sides. TQ 17.3 Take the square root of both sides. Step 3Find the length. QR= 2(17.3) = 34.6

  23. Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find mTRQ.

  24. Lesson Quiz: Part II Find each measure. 2. NGH 3. HL

  25. Lesson Quiz: Part III 4. T U, and AC = 47.2. Find PL to the nearest tenth.

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