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Find Arc Measures

Find Arc Measures. Lesson 6.2 Page 191. Definitions. Central Angle- and angle whose vertex is the center of the circle. Minor Arc- an arc measure less than 180˚. Major Arc- an arc measure more than 180˚. Measuring Arcs. The measure of a minor arc is equal to its central angle.

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Find Arc Measures

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  1. Find Arc Measures Lesson 6.2 Page 191

  2. Definitions • Central Angle- and angle whose vertex is the center of the circle. • Minor Arc- an arc measure less than 180˚. • Major Arc- an arc measure more than 180˚.

  3. Measuring Arcs • The measure of a minor arc is equal to its central angle. • The measure of a major arc is equal to 360˚ - minor arc associated with it.

  4. Find the measure of each arc of P, where RTis a diameter. c. a. RTS RST RS b. a. RSis a minor arc, so mRS=mRPS=110o. b. – RTSis a major arc, so mRTS = 360o 110o = 250o. c. RT is a diameter, so RSTis a semicircle, and mRST=180o. EXAMPLE 1 Find measures of arcs SOLUTION

  5. Survey a. = + A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. a. mAC mAB mBC mAC EXAMPLE 2 Find measures of arcs SOLUTION = 29o + 108o = 137o

  6. Survey b. A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. mACD = mAC + mCD b. mACD EXAMPLE 2 Find measures of arcs SOLUTION = 137o + 83o = 220o

  7. Survey – mADC = 360o A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. c. mAC c. mADC EXAMPLE 2 Find measures of arcs SOLUTION = 360o – 137o = 223o

  8. Survey A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. mEBD = 360o – mED d. d. mEBD EXAMPLE 2 Find measures of arcs SOLUTION = 360o – 61o = 299o

  9. for Examples 1 and 2 GUIDED PRACTICE Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc.

  10. 1 . TQ TQis a minor arc, so m TQ=120o. 2 . QRT QRTis a major arc, so m QRT=240o. for Examples 1 and 2 GUIDED PRACTICE SOLUTION SOLUTION

  11. 3 TQRis a semicircle, so m TQR =180o. 4 . TQR . QS QSis a minor arc, so m QS =160o. for Examples 1 and 2 GUIDED PRACTICE SOLUTION SOLUTION

  12. 5 TSis a minor arc, so m TS =80o. 6 . TS . RST RSTis a semicircle, so m RST =180o. for Examples 1 and 2 GUIDED PRACTICE SOLUTION SOLUTION

  13. a. b. a. CDEF because they are in the same circle and mCD = mEF b. RSand TUhave the same measure, but are not congruent because they are arcs of circles that are not congruent. EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

  14. a. b. a. CDEF because they are in the same circle and mCD = mEF b. RSand TUhave the same measure, but are not congruent because they are arcs of circles that are not congruent. EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

  15. VXYZ because they are in congruent circles and mVX=mYZ . c. c. EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

  16. ABCD because they are in congruent circles and mAB=mCD . 7. for Example 3 GUIDED PRACTICE Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

  17. 8. MNand PQhave the same measure, but are not congruent because they are arcs of circles that are not congruent. for Example 3 GUIDED PRACTICE Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

  18. Homework 6.2 • Exercise set B page 195 • 1-41 odd

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