9 6 Other Angles

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9 6 Other Angles

  1. 1. 9-6 Other Angles
  2. 2. Don’t write this down yet!!!!!! <ul><li>Lines intersecting in and out of a circle – Two lines can intersect in three different places: ON a circle INSIDE or OUTSIDE </li></ul>
  3. 3. <ul><li>Lines intersecting in and out of a circle </li></ul><ul><ul><li>INSIDE </li></ul></ul>Theorem Each angle is ½ of the sum of the intercepted arcs. A B D C 1 1 2 2 m  1 = ½(m CD + m AB ) m  2 = ½(mBC + mAD)
  4. 4. <ul><li>Lines intersecting in and out of a circle </li></ul><ul><ul><li>OUTSIDE </li></ul></ul>Theorem The angle is ½ of the difference of the intercepted arcs. A B C 1 m  1 = ½(m BC - m AC )
  5. 5. <ul><li>Lines intersecting in and out of a circle </li></ul><ul><ul><li>OUTSIDE </li></ul></ul>Theorem Each angle is ½ of the difference of the intercepted arcs. P Q R 2 m  2 = ½(m PQR - m PR )
  6. 6. <ul><li>Lines intersecting in and out of a circle </li></ul><ul><ul><li>OUTSIDE </li></ul></ul>Theorem Each angle is ½ of the difference of the intercepted arcs. W Y Z 3 m  3 = ½(m XY - m WZ ) X
  7. 7. Practice T Q R P m  PRQ = 130 ° m RTQ = ???????? 130 °
  8. 8. Practice T Q R P m  PRQ = 130 ° m RTQ = 2(130 °) = 260° 130 °
  9. 9. Practice E H G D Solve for x (arc GF) 200 ° 72 ° x ° F
  10. 10. Practice E H G D Solve for x 200 ° 72 ° x ° m  GHF = ½(mEDG - mGF) 72 ° = ½(200 ° - x ° ) 144° = 200° - x° x = 56 F
  11. 11. SPICSA Page 360 2-20 even

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