1. 12-2
Arcs and Chords
Holt McDougal Geometry
Holt Geometry

2. Learning Targets
I will apply properties of arcs and chords.

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

4. A central angle is an angle whose vertex is the center of a circle
A central angle is an angle whose vertex is the center of a circle. An arc is 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 are named by the two endpoints of the arc. Major arcs and semicircles must be named by three points, with the endpoints being the first and third points named.

7. Example 1: Data Application
The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.
mKLF = 360° – mKJF
mKJF = 0.35(360)
= 126
mKLF = 360° – 126°
= 234

8. Check It Out! 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 .
b. mAHB
= 360° – mAMB
c. mEMD
= 0.10(360)
mAHB
= 360° – 0.25(360)
= 36
= 270
Central  is 10% of the .

9. Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.

10. Example 2: Using the Arc Addition Postulate
Find mBD.
mBC = 97.4
Vert. s Thm.
mCFD = 180 – (97.4 + 52)
= 30.6
∆ Sum Thm.
mCD = 30.6
mCFD = 30.6
mBD = mBC + mCD
Arc Add. Post.
= 97.4 
Substitute.
Simplify.
= 128

11. Check It Out! Example 2a
Find each measure.
mJNL
180° + 40° = 220°

12. Check It Out! Example 2b
Find each measure.
mLJN
mLJN = 360° – ( )°
= 295°

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

15. Example 3A: Applying Congruent Angles, Arcs, and Chords
TV  WS. Find mWS.
TV  WS
 chords have  arcs.
mTV = mWS
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.
mWS = 7(11) + 11
Substitute 11 for n.
= 88°
Simplify.

16. Example 3B: Applying Congruent Angles, Arcs, and Chords
C  J, and mGCD  mNJM. Find NM.
GCD  NJM
GD  NM
 arcs have  chords.
GD  NM
GD = NM
Def. of  chords

17. Example 3B Continued
C  J, and mGCD  mNJM. Find NM.
14t – 26 = 5t + 1
9t = 27
t = 3
NM = 5(3) + 1
= 16

18. Check It Out! Example 3a
PT bisects RPS. Find RT.
RPT  SPT
mRT  mTS
RT = TS
6x = 20 – 4x
10x = 20
x = 2
RT = 6(2)
RT = 12

19. Check It Out! Example 3b
Find each measure.
A  B, and CD  EF. Find mCD.
mCD = mEF
25y = (30y – 20)
20 = 5y
4 = y
CD = 25(4)
mCD = 100

21. Example 4: Using Radii and Chords
Find NP.
Step 1 Draw radius RN.
RN = 17
Step 2 Use the Pythagorean Theorem.
SN2 + RS2 = RN2
SN = 172
SN2 = 225
SN = 15
Step 3 Find NP.
NP = 2(15) = 30

22. HOMEWORK:
Pg 806, #5 – 18.