9-3 Arcs and Central Angles
How many degrees in a circle? <ul><li>90 </li></ul><ul><li>270 </li></ul><ul><li>300 </li></ul><ul><li>360 </li></ul><ul><...
<ul><li>Central Angle </li></ul><ul><ul><li>An angle whose vertex is the center of a circle </li></ul></ul>9-3 Arcs and Ce...
<ul><li>Minor Arc </li></ul><ul><ul><li>If the central angle is < 180º  </li></ul></ul><ul><ul><li>A to B  on the circle  ...
<ul><li>Major Arc </li></ul><ul><ul><li>If the central angle is > 180º  </li></ul></ul><ul><ul><li>A to B  on the circle  ...
<ul><li>Semicircle </li></ul><ul><ul><li>If the central angle is 180º </li></ul></ul>P A B 9-3 Arcs and Central Angles
<ul><li>Measuring Arcs </li></ul><ul><ul><li>The measure of a minor arc is the measure of its central angle. </li></ul></u...
<ul><li>Measuring Arcs </li></ul><ul><ul><li>The measure of a major arc is 360º minus the central angle. </li></ul></ul>P ...
What is the measure of AB? <ul><li>280 </li></ul><ul><li>360 </li></ul><ul><li>80 </li></ul><ul><li>120 </li></ul><ul><li>...
What is the measure of ACB? <ul><li>280 </li></ul><ul><li>360 </li></ul><ul><li>80 </li></ul><ul><li>120 </li></ul><ul><li...
What is the measure of AB? <ul><li>270 </li></ul><ul><li>80 </li></ul><ul><li>80 </li></ul><ul><li>14 </li></ul><ul><li>90...
<ul><li>Arc Addition Postulate </li></ul><ul><ul><li>The measure of two adjacent arcs is the addition of each arc. </li></...
<ul><li>Theorem </li></ul><ul><ul><li>In the same circle or    circles, two minor arcs are    if and only if their corre...
SPICSA P 341  2,4,6,8,10,11,14,16 (Don’t skimp on the proof)
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9 3 Arcs And Central Angles Filled Out

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9 3 Arcs And Central Angles Filled Out

  1. 1. 9-3 Arcs and Central Angles
  2. 2. How many degrees in a circle? <ul><li>90 </li></ul><ul><li>270 </li></ul><ul><li>300 </li></ul><ul><li>360 </li></ul><ul><li>380 </li></ul><ul><li>400 </li></ul><ul><li>720 </li></ul>0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
  3. 3. <ul><li>Central Angle </li></ul><ul><ul><li>An angle whose vertex is the center of a circle </li></ul></ul>9-3 Arcs and Central Angles P A B Central Angle
  4. 4. <ul><li>Minor Arc </li></ul><ul><ul><li>If the central angle is < 180º </li></ul></ul><ul><ul><li>A to B on the circle in the angle </li></ul></ul>P A B C Name: AB 9-3 Arcs and Central Angles
  5. 5. <ul><li>Major Arc </li></ul><ul><ul><li>If the central angle is > 180º </li></ul></ul><ul><ul><li>A to B on the circle outside the angle </li></ul></ul>P A B C Name: ACB 9-3 Arcs and Central Angles
  6. 6. <ul><li>Semicircle </li></ul><ul><ul><li>If the central angle is 180º </li></ul></ul>P A B 9-3 Arcs and Central Angles
  7. 7. <ul><li>Measuring Arcs </li></ul><ul><ul><li>The measure of a minor arc is the measure of its central angle. </li></ul></ul>P A B C mAB = 60º 60º 60º 9-3 Arcs and Central Angles Key Point
  8. 8. <ul><li>Measuring Arcs </li></ul><ul><ul><li>The measure of a major arc is 360º minus the central angle. </li></ul></ul>P A B C mACB = 300º 60º 60º 9-3 Arcs and Central Angles
  9. 9. What is the measure of AB? <ul><li>280 </li></ul><ul><li>360 </li></ul><ul><li>80 </li></ul><ul><li>120 </li></ul><ul><li>90 </li></ul><ul><li>70 </li></ul>A B C 280º 7 √2 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
  10. 10. What is the measure of ACB? <ul><li>280 </li></ul><ul><li>360 </li></ul><ul><li>80 </li></ul><ul><li>120 </li></ul><ul><li>90 </li></ul><ul><li>70 </li></ul>A B C 280º 7 √2 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
  11. 11. What is the measure of AB? <ul><li>270 </li></ul><ul><li>80 </li></ul><ul><li>80 </li></ul><ul><li>14 </li></ul><ul><li>90 </li></ul><ul><li>7 </li></ul>A B C 270º 7 √2 0 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
  12. 12. <ul><li>Arc Addition Postulate </li></ul><ul><ul><li>The measure of two adjacent arcs is the addition of each arc. </li></ul></ul>P A B C mABC = mAB + m BC 9-3 Arcs and Central Angles
  13. 13. <ul><li>Theorem </li></ul><ul><ul><li>In the same circle or  circles, two minor arcs are  if and only if their corresponding central angles are  . </li></ul></ul>P A B C AB  BC if and only if 9-3 Arcs and Central Angles
  14. 14. SPICSA P 341 2,4,6,8,10,11,14,16 (Don’t skimp on the proof)

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