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Review. 14-6 Congruent Arcs. More about Arcs, Angles and Chords (oh my!). In the same circle, or in congruent circles, two arcs are called congruent if they have the same measure. B. A. C. D. Theorem 14-17

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Review

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  1. Review

  2. 14-6 Congruent Arcs More about Arcs, Angles and Chords (oh my!)

  3. In the same circle, or in congruent circles, two arcs are called congruent if they have the same measure. B A C D

  4. Theorem 14-17 • In the same circle or in congruent circles, if two chords are congruent, then so are the corresponding minor arcs. A A' r s P' B' P B

  5. Theorem 14-18 • In the same circle or in congruent circles, if two arcs are congruent, then so are the corresponding chords. A C B D

  6. Theorem 14-19 The Tangent-Secant Theorem • Given an angle with its vertex on a circle, formed by a secant ray and a tangent ray. The measure of the angle is half the measure of the intercepted arc. A X B

  7. For any angle whose vertex is on the circle the measure of the angle is half of the intercepted arc.

  8. Secant-Secant theorem Vertex is inside of the circle • X=1/2(Y + Z) Z Y X

  9. X Y Z 3 cases Vertex is outside the circle • X=1/2(Y-Z) X Z Y Y X Z

  10. Pg. 478 (1,3-5,8, 11bc,13bc, 15,18,22,25)

  11. Entry 120 Find x 1. 2. 3. 4. x 147 150 x 95 x x 40 145

  12. 5. Two points on a circle determine a minor arc and a major arc. If the major arc is 20 less than three times the minor arc, what is the measure of the major arc? 6. AB is the diameter of a circle and chords AC and BD intersect at E. If mAD = 85 and mBC = 70, what is m<AEB?

  13. Pg. 478(2,11a,d,13a,d,23) Pg. 475(10,15,17b,d)

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