Find Arc Measures Warm Up Lesson Presentation Lesson Quiz

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

Example 1 Find the measure of each arc of P, where RT is a diameter. RS a. RTS b. RST c. SOLUTION RS is a minor arc, so mRS = m RPS = 110o. a. RTS is a major arc, so mRTS = 360o 110o = 250o. b. – c. RT is a diameter, so RST is a semicircle, and mRST = 180o.

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

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

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

Example 2 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. Survey d. mEBD SOLUTION d. mEBD = 360o – mED = 360o – 61o = 299o

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

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

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

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

Example 3 Tell whether the red arcs are congruent. Explain why or why not. b. SOLUTION b. RS and TU have 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. c. SOLUTION c. VX YZ because they are in congruent circles and mVX = mYZ .

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

Guided Practice Tell whether the red arcs are congruent. Explain why or why not. 8. ANSWER Not congruent: MN and PQ have the same measure, but they are not congruent because the two circles are not congruent.

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

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

Two diameters of P are AB and CD.If m = 50 , find m and m . . AD Lesson Quiz 5. ACD AC Two diameters of P are AB and CD.If m = 50 , find m and m . . AD o ANSWER o 310 ; 130