1. 10.2 Arcs and chords Pg 603

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

3. Arcs 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 180 o (named by 2 letters). A B B P BP (

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

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

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

7. Post. 26 arc addition postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs. A B C m ABC = m AB+ m BC ( ((

8. Congruency among arcs Congruent arcs- 2 arcs with the same measure MUST be from the same circle OR  circles!!!

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

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

11. Thm 10.4 In the same circle (or in  circles), 2 minor arcs are  iff their corresponding chords are . A B C AB  BC iff AB  BC ((

12. Thm 10.5 If a diameter of a circle is  to a chord, then the diameter bisects the chord and its arc. E D G C F If EG is  to DF, then DC  CF and DG  GF ((

13. If JK is a  bisector of ML, then JK is a diameter. Thm 10.6 If one chord is a  bisector of another chord then the 1 st chord is a diameter. J K L M

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

15. Thm10.7 In the same circle (or in  circles), 2 chords are  iff they are =dist from the center. DC A G F EB DE  CB iff AG  AF

16. Ex: find CG. A B C E F D 6 6 6 6 7 G 7 2 =CF 2 +6 2 49=CF 2 +36 13=CF 2 CF  CG CF = ð13  CG = ð13

17. Assignment