1. Splash Screen

2. Five-Minute Check (over Lesson 10–5) CCSS 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. Determine whether BC is tangent to the given circle.
___
A. yes
B. no
5-Minute Check 1

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

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

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

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

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

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

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

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

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

13. Mathematical Practices
Content Standards
Reinforcement of G.C.4 Construct a tangent line from a point outside a given circle to the circle.
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
1 Make sense of problems and persevere in solving them.
CCSS

14. You found measures of segments formed by tangents to a circle.
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

15. secant
Vocabulary

16. Concept

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

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

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

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

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

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

23. Subtract 25 from each side.
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

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

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

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

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

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

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

30. Concept

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

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

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

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

35. A. Find mFGI.
A. 98
B. 108 C D
Example 2

36. A. Find mFGI.
A. 98
B. 108 C D
Example 2

37. B.
A. 99 B
C. 162
D. 198
Example 2

38. B.
A. 99 B
C. 162
D. 198
Example 2

39. Concept

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

55. Concept

56. End of the Lesson