1. Lesson 6.2 Find Arc Measures
Pg 191

2. Central angle
Central angle- angle whose vertex is the center of a circle A
ACB is a central angle C B

3. Arcs A Arc- a piece of a circle. Named with 2 or 3 letters
Measured in degrees
Minor arc- part of a circle that measures less than 180o (named by 2 letters). B B ( BP P

4. More arcs
Major arc- part of a circle that measures between 180o and 360o.
(needs three letters to name)
Semicircle- an arc whose endpts
are the endpts of a diameter of the circle
(OR ½ of a circle)
(need 3 letters to name) A ( (
ABC or CBA B C C S

5. Arc measures Measure of a minor arc- measure of its central 
Measure of a major arc- 360o minus measure of minor arc

6. Ex: find the arc measures(
m AB=
m BC=
m AEC=
m BCA=
50o (
130o ( A
180o
180o D (
180o+130o = 310o
50o
130o C
OR 360o- 50o = 310o B

7. Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs. B A ( ( ( C
m ABC = m AB+ m BC

8. Congruency among arcs
Congruent circles are two circles with the same radius
Congruent arcs- 2 arcs with the same measure that are arcs of the same circle or congruent circles!!!

9. Example (
m AB=30o A (
m DC=30o E
30o B D ( (
30o DC C

10. Ex: continued ( ( ( ( m BD= 45o A m AE= 45o B BD @ AE
The arcs are the same measure; so, why aren’t they ?
45o C D E
The 2 circles are NOT  !

11. Lesson 6.3 Apply Properties of Chords
Page 198

12. Theorem 6.5
In the same circle (or in congruent circles), 2 minor arcs are congruent if and only if their corresponding chords are congruent. A ( (
BC iff BC B C

13. Theorem 6.6
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. M
If JK is a  bisector of ML, then JK is a diameter. K J L

14. Theorem 6.7
If a diameter of a circle is  to a chord, then the diameter bisects the chord and its arc.
If EG is  to DF, then CF and GF ( ( E C D F G

15. Ex: find m BC ( ( ( B By thm 10.4 BD @ BC. 3x+11 2x+47 3x+11=2x+47
2(36)+47
72+47 A
119o D C

16. Theorem 6.8
In the same circle (or in  circles), 2 chords are  iff they are =dist from the center. D C
CB iff AF G F A E B

17. Ex: find CG. CF @ CG B 6 72=CF2+62 G 49=CF2+36 6 A 13=CF2 CF = √13 C