1. Splash Screen

2. Five-Minute Check (over Lesson 10–4) CCSS Then/Now New Vocabulary
Example 1: Identify Common Tangents
Theorem 10.10
Example 2: Identify a Tangent
Example 3: Use a Tangent to Find Missing Values
Theorem 10.11
Example 4: Use Congruent Tangents to Find Measures
Example 5: Real-World Example: Find Measures in Circimscribed Polygons
Lesson Menu

3. Refer to the figure. Find m1.
A. 60
B. 55
C. 50
D. 45
5-Minute Check 1

4. Refer to the figure. Find m2.
A. 30
B. 25
C. 20
D. 15
5-Minute Check 2

5. Refer to the figure. Find m3.
A. 35
B. 30
C. 25
D. 20
5-Minute Check 3

6. Refer to the figure. Find m4.
A. 120
B. 100
C. 80
D. 60
5-Minute Check 4

7. find x if mA = 3x + 9 and mB = 8x – 4.
C. 12
D. 13
5-Minute Check 5

8. The measure of an arc is 95°
The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it?
A. 47.5°
B. 95°
C. 190°
D. 265°
5-Minute Check 6

9. Mathematical Practices
Content Standards
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
G.C.4 Construct a tangent line from a point outside a given circle to the circle.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
CCSS

10. Use properties of tangents.
You used the Pythagorean Theorem to find side lengths of right triangles.
Use properties of tangents.
Solve problems involving circumscribed polygons.
Then/Now

11. tangent
point of tangency
common tangent
Vocabulary

12. Identify Common Tangents
A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent.
Answer: These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.
Example 1

13. Answer: These circles have 2 common tangents.
Identify Common Tangents
B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent.
Answer: These circles have 2 common tangents.
Example 1

14. A. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.
A. 2 common tangents
B. 4 common tangents
C. 6 common tangents
D. no common tangents
Example 1

15. B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.
A. 2 common tangents
B. 3 common tangents
C. 4 common tangents
D. no common tangents
Example 1

16. Concept

17. Test to see if ΔKLM is a right triangle.
Identify a Tangent
Test to see if ΔKLM is a right triangle. ?
= 292 Pythagorean Theorem
841 = 841 Simplify.
Answer:
Example 2

18. A. B.
Example 2

19. EW 2 + DW 2 = DE 2 Pythagorean Theorem
Use a Tangent to Find Missing Values
EW 2 + DW 2 = DE 2 Pythagorean Theorem
242 + x 2 = (x + 16)2 EW = 24, DW = x, and DE = x + 16
576 + x 2 = x x Multiply.
320 = 32x Simplify.
10 = x Divide each side by 32.
Answer: x = 10
Example 3

20. A. 6
B. 8
C. 10
D. 12
Example 3

21. Concept

22. AC = BC Tangents from the same exterior point are congruent.
Use Congruent Tangents to Find Measures
AC = BC Tangents from the same exterior point are congruent.
3x + 2 = 4x – 3 Substitution
2 = x – 3 Subtract 3x from each side.
5 = x Add 3 to each side.
Answer: x = 5
Example 4

23. A. 5
B. 6
C. 7
D. 8
Example 4

24. Step 1 Find the missing measures.
Find Measures in Circumscribed Polygons
Step 1 Find the missing measures.
Example 5

25. Step 2 Find the perimeter of ΔQRS.
Find Measures in Circumscribed Polygons
Step 2 Find the perimeter of ΔQRS.
= or 36 cm
Answer: So, the perimeter of ΔQRS is 36 cm.
Example 5

26. A. 42 cm
B. 44 cm
C. 48 cm
D. 56 cm
Example 5

27. End of the Lesson