14 3 secant angles lesson
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14 3 secant angles lesson

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14 3 secant angles lesson 14 3 secant angles lesson Presentation Transcript

  • LESSON 14-3: A CAN’T, B CAN’T, SECANT!!!
  • 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.
  • 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.
  • 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.
  • SECANTS, TANGENTS AND ANGLES • So let’s solve for the angles below. A C B D X 40⁰ 110⁰ 50⁰ 160⁰
  • SECANTS, TANGENTS AND ANGLES • What about this? Could you find ALL interior angles? A C B D X 35⁰ 65⁰
  • 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?
  • 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.
  • SECANTS, TANGENTS AND ANGLES • Using the given information, find all missing angles and arcs in the figure below. 120⁰
  • 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?
  • SECANTS, TANGENTS AND ANGLES • These angles can be formed of the intersections of two secants, two tangents or one of each.
  • 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.
  • SECANTS, TANGENTS AND ANGLES • Find the measure of angle P below. P 30⁰ 100⁰
  • SECANTS, TANGENTS AND ANGLES • Find the measure of angle P below. P 30⁰ 100⁰ M<P = 35
  • SECANTS, TANGENTS AND ANGLES • Find the measure of arc PO below… P 30⁰ 40⁰ O
  • SECANTS, TANGENTS AND ANGLES • Find the measure of arc PO below… P 30⁰ 40⁰ O
  • SECANTS, TANGENTS AND ANGLES • Today, you will need to use the information I have given you in many ways!