1. Arcs and Central Angles
Section 9-3:
Arcs and Central Angles

2. 1. central angle: an angle with its ___________ _______________________________________ 2. arc: an ______________________________ 3. ________ is an arc measuring less than half the circle. (Use 2 letters when naming).
vertex at
the center of the circle.
unbroken part of a circle.
Minor

3. 4. ________ is an arc measuring more than half the circle
4. ________ is an arc measuring more than half the circle. (Use 3 letters when naming). 5. ____________ is an arc measuring exactly 180° or half the circle. (Use 3 letters when naming). 6. If C and B are the endpoints of a diameter, then the two arcs are called ____________.
Major
Semicircles
semicircles

4. 7. List examples of minor arcs: ______________ 8
7. List examples of minor arcs: ______________ 8. List examples of major arcs: ______________ ____________________ 9. List examples of semi-circles: _____________
𝐴𝐵 , 𝐵𝐷 , 𝐷𝐶 , 𝐶𝐴
𝐴𝐵𝐶 , 𝐴𝐷𝐶 ,
𝐵𝐷𝐴 , 𝐵𝐶𝐴
𝐶𝐴𝐵 , 𝐵𝐷𝐶

5. 10. _____________ are arcs that have exactly one point in common
10. _____________ are arcs that have exactly one point in common. They do not overlap. 11. List examples of adjacent arcs: _________________________________ 12. _______________ are arcs, in the same circle or in congruent circles, that have equal measures.
Adjacent arcs
𝐴𝐵 𝑎𝑛𝑑 𝐵𝐷 ; 𝐵𝐷𝐶 and 𝐶𝐴
Congruent arcs

6. Postulate 16 – Arc Addition Postulate
The measure of the arc formed by two ___________ arcs is the _____ ___ ______
___________ ___ ______ _____ _____.
adjacent
sum of
the
measures of
these
two
arcs

7. * The measure of a minor arc is the measure of its central angle.
13. m 𝐴𝐵 = _____ m 𝐶𝐴𝐵 = _____  
15. m 𝐴𝐶 = _____ m 𝐶𝐷𝐵 = _____
17. mAOC = _____ mBOC = _____
19. m 𝐴𝐶𝐵 = _____ m 𝐴𝐵𝐶 = _____
60°
180°
120°
180°
120°
180°
300°
240°
120°
60°
120°

8. 130°
72°
50°

9. 150°
30°
150°
95°

10. 4x = 4(26) = 104
2x – 14 = 2(26) – 14 = 38
2x = 2(26) = 52 38
3x + 10 = 3(26) + 10 = 88
104 52
3x = 3(26) = 78 88 78
4x + 2x – x + 3x x = 360
14x – 4 = 360
14x = 364
x = 26

11. = 88⁰
= 52⁰
= 38⁰
= 104⁰
= 78⁰
= 166⁰
= 322⁰

12. HOMEWORK: page 341 #1-13 all (CE)