1. Find Arc Measures
Warm Up
Lesson Presentation
Lesson Quiz

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

3. 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 o = 250o. b. – c.
RT is a diameter, so RST is a semicircle, and mRST = 180o.

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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.

13. 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 .

14. 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

15. 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.

16. 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

17. 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

18. 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