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Warm Up

Find Arc Measures. Warm Up. Lesson Presentation. Lesson Quiz. Find x and y. 1. x = 60; y = 60. ANSWER. 2. x = 35; y = 35. ANSWER. Warm-Up. Find the measure of each arc of P , where RT is a diameter. c. a. RTS. RST. RS. b. a.

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Warm Up

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  1. Find Arc Measures Warm Up Lesson Presentation Lesson Quiz

  2. Find xand y. 1. x = 60; y = 60 ANSWER 2. x = 35; y = 35 ANSWER Warm-Up

  3. 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 SOLUTION

  4. 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. = + a. mAC mAB mBC mAC Example 2 Survey SOLUTION = 29o + 108o = 137o

  5. 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. b. mACD = mAC + mCD b. mACD Example 2 Survey SOLUTION = 137o + 83o = 220o

  6. 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. – mADC = 360o c. mAC c. mADC Example 2 Survey SOLUTION = 360o – 137o =223o

  7. 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 Survey SOLUTION = 360o – 61o = 299o

  8. 1 . TQ ANSWER minor arc; 120° 2 . QRT ANSWER major arc; 240° Guided Practice Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc.

  9. 3 4 ANSWER semicircle; 180° . TQR . QS ANSWER minor arc; 160° Guided Practice Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc.

  10. 5 6 ANSWER minor arc; 80° . TS . RST ANSWER semicircle; 180° Guided Practice Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc.

  11. a. a. CDEF because they are in the same circle and mCD = mEF Example 3 Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

  12. b. b. RSand TUhave the same measure, but are not congruent because they are arcs of circles that are not congruent. Example 3 Tell whether the red arcs are congruent. Explain why or why not. SOLUTION

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

  14. 7. ANSWER Congruent; ABCD since the two circles are congruent and mAB=mCD. Guided Practice Tell whether the red arcs are congruent. Explain why or why not.

  15. 8. ANSWER Not congruent: MNand PQhave the same measure, but they are not congruent because the two circles are not congruent. Guided Practice Tell whether the red arcs are congruent. Explain why or why not.

  16. 2. CBE 1. 3. BCE BC o o o ANSWER ANSWER ANSWER semicircle, 180 major arc, 212 minor arc, 32 Lesson Quiz Describe each figure as a minor arc, major arc or a semicircle. Find the arc measure.

  17. ~ ~ Explain why AE BC. 4. = = BC BC AE AE ANSWER mAFE = m BFC because the angles are vertical angles, so AFEBFC.Then arcs and are arcs that have the same measure in the same circle. By definition . Lesson Quiz

  18. 5. . o Two diameters ofPareABandCD.If m = 50 , find m and m . AC AD ACD o o ANSWER 310 ; 130 Lesson Quiz

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