14 3 secant angles lesson

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14 3 secant angles lesson

  1. 1. LESSON 14-3: A CAN’T, B CAN’T, SECANT!!!
  2. 2. SECANTS, TANGENTS AND ANGLES • Up until now, we have discussed the tangents and inscribed angles of certain circles. • Now, we can discuss secants and the angles created by them.
  3. 3. SECANTS, TANGENTS AND ANGLES • Like a tangent line, we judge a secant line by the number of times it intersects the circle. • THE NUMBER IS TWO!!! • When two secant lines intersect inside a circle then the angle formed is related to the arcs they intercepts.
  4. 4. SECANTS, TANGENTS AND ANGLES • Theorem 14-8: If two secants or chords intersect in the interior of a circle, then the measure of an angle formed is one half the sum of the measure of the arcs intercepted by the angle and it’s vertical angle.
  5. 5. SECANTS, TANGENTS AND ANGLES • So let’s solve for the angles below. A C B D X 40⁰ 110⁰ 50⁰ 160⁰
  6. 6. SECANTS, TANGENTS AND ANGLES • What about this? Could you find ALL interior angles? A C B D X 35⁰ 65⁰
  7. 7. SECANTS, TANGENTS AND ANGLES • Not only to secants interact with each other. • Secants and tangents can intersect each other too! • What is the relationship here?
  8. 8. SECANTS, TANGENTS AND ANGLES • If a secant and tangent intersect at the point of tangency, then the measure of the angles will be half the measure of the arcs they intersect.
  9. 9. SECANTS, TANGENTS AND ANGLES • Using the given information, find all missing angles and arcs in the figure below. 120⁰
  10. 10. SECANTS, TANGENTS AND ANGLES • So we’ve dealt with angles on the interior of a circle and ones directly on the circle… • ..but what about those on the exterior of a circle?
  11. 11. SECANTS, TANGENTS AND ANGLES • These angles can be formed of the intersections of two secants, two tangents or one of each.
  12. 12. SECANTS, TANGENTS AND ANGLES • Theorem 14-9: When any of these is the case, the angle measure can be found by taking half the difference of the two intercepted arcs.
  13. 13. SECANTS, TANGENTS AND ANGLES • Find the measure of angle P below. P 30⁰ 100⁰
  14. 14. SECANTS, TANGENTS AND ANGLES • Find the measure of angle P below. P 30⁰ 100⁰ M<P = 35
  15. 15. SECANTS, TANGENTS AND ANGLES • Find the measure of arc PO below… P 30⁰ 40⁰ O
  16. 16. SECANTS, TANGENTS AND ANGLES • Find the measure of arc PO below… P 30⁰ 40⁰ O
  17. 17. SECANTS, TANGENTS AND ANGLES • Today, you will need to use the information I have given you in many ways!

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