1. Five-Minute Check (over Lesson 9–5) Mathematical Practices Then/Now
New Vocabulary
Theorem 9.12
Example 1: Use Intersecting Chords or Secants
Theorem 9.13
Example 2: Use Intersecting Secants and Tangents
Theorem 9.14
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

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

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

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

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

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

7. Mathematical Practices
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. MP

8. 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

9. secant
Vocabulary

10. Concept

11. 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

12. 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

13. 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

14. 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

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

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

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

18. Concept

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

20. 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

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

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

23. Concept

24. 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

25. 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

26. 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

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

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

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

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

31. 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

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

33. Concept