1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 10–5) 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

3. Over Lesson 10–5 5-Minute Check 1 A.yes B.no Determine whether BC is tangent to the given circle. ___

4. Over Lesson 10–5 5-Minute Check 2 A.yes B.no Determine whether QR is tangent to the given circle. ___

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

6. Over Lesson 10–5 5-Minute Check 4 Find x. Assume that segments that appear to be tangent are tangent. A. B. C.20 D.

7. Over Lesson 10–5 5-Minute Check 5 SL and SK are tangent to the circle. Find x. ___ A.1 B. C.5 D.44 __ 5 2

8. Then/Now 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.

9. Vocabulary secant

10. Concept

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

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

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

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

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

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

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

18. Concept

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

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

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

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

23. Concept

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

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

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

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

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

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

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

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

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

33. Concept

34. End of the Lesson