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Splash Screen. Five-Minute Check (over Lesson 10–5) NGSSS Then/Now New Vocabulary Theorem 10.12 Example 1: Use Intersecting Chords or Secants Theorem 10.13 Example 2: Use Intersecting Secants and Tangents Theorem 10.14 Example 3: Use Tangents and Secants that Intersect Outside a Circle

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–5) NGSSS Then/Now New Vocabulary Theorem 10.12 Example 1: Use Intersecting Chords or Secants Theorem 10.13 Example 2: Use Intersecting Secants and Tangents Theorem 10.14 Example 3: Use Tangents and Secants that Intersect Outside a Circle Example 4: Real-World Example: Apply Properties of Intersecting Secants Concept Summary: Circle and Angle Relationships Lesson Menu

  3. A B ___ Determine whether BC is tangent to the given circle. A. yes B. no 5-Minute Check 1

  4. A B ___ Determine whether QR is tangent to the given circle. A. yes B. no 5-Minute Check 2

  5. A B C D Find x. Assume that segments that appear to be tangent are tangent. A. 10 B. 11 C. 12 D. 13 5-Minute Check 3

  6. A B C D A. B. C.20 D. Find x. Assume that segments that appear to be tangent are tangent. 5-Minute Check 4

  7. A B C D ___ ___ SL and SK are tangent to the circle. Find x. A.1 B. C.5 D.44 5 __ 2 5-Minute Check 5

  8. MA.912.G.6.2Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles. MA.912.G.6.4 Determine and use measures of arcs and related angles. Also addresses MA.912.G.6.3. NGSSS

  9. You found measures of segments formed by tangents to a circle. (Lesson 10–5) • Find measures of angles formed by lines intersecting on or inside a circle. • Find measures of angles formed by lines intersecting outside the circle. Then/Now

  10. secant Vocabulary

  11. Concept

  12. Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer:x = 82 Example 1

  13. Use Intersecting Chords or Secants B. Find x. Step 1Find mVZW. Theorem 10.12 Substitution Simplify. Example 1

  14. Use Intersecting Chords or Secants Step 2Find mWZX. WZX = 180 – VZWDefinition of supplementary angles x = 180 – 79Substitution x = 101 Simplify. Answer:x = 101 Example 1

  15. Use Intersecting Chords or Secants C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Subtract 25 from each side. Answer:x = 95 Example 1

  16. A B C D A. Find x. A. 92 B. 95 C. 98 D. 104 Example 1

  17. A B C D B. Find x. A. 92 B. 95 C. 97 D. 102 Example 1

  18. A B C D C. Find x. A. 96 B. 99 C. 101 D. 104 Example 1

  19. Concept

  20. Use Intersecting Secants and Tangents A. Find mQPS. Theorem 10.13 Substitute and simplify. Answer:mQPS= 125 Example 2

  21. B. Answer: Use Intersecting Secants and Tangents Theorem 10.13 Substitution Multiply each side by 2. Example 2

  22. A B C D A. Find mFGI. A. 98 B. 108 C. 112.5 D. 118.5 Example 2

  23. A B C D B. A. 99 B. 148.5 C. 162 D. 198 Example 2

  24. Concept

  25. A. Use Tangents and Secants that Intersect Outside a Circle Theorem 10.14 Substitution Multiply each side by 2. Example 3

  26. Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1. Example 3

  27. B. Use Tangents and Secants that Intersect Outside a Circle Theorem 10.14 Substitution Multiply each side by 2. Example 3

  28. Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side. Example 3

  29. A B C D A. A. 23 B. 26 C. 29 D. 32 Example 3

  30. A B C D B. A. 194 B. 202 C. 210 D. 230 Example 3

  31. Apply Properties of Intersecting Secants Theorem 10.14 Substitution Example 4

  32. Apply Properties of Intersecting Secants Multiply each side by 2. Subtract 96 from each side. Multiply each side by –1. Example 4

  33. A B C D A. 25 B. 35 C. 40 D. 45 Example 4

  34. Concept

  35. End of the Lesson

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