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Five-Minute Check (over Lesson 10–4)
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
Over Lesson 10–4
A. 60
B. 55
C. 50
D. 45
Refer to the figure. Find m1.
Over Lesson 10–4
A. 30
B. 25
C. 20
D. 15
Refer to the figure. Find m2.
Over Lesson 10–4
A. 35
B. 30
C. 25
D. 20
Refer to the figure. Find m3.
Over Lesson 10–4
A. 120
B. 100
C. 80
D. 60
Refer to the figure. Find m4.
Over Lesson 10–4
A. 10
B. 11
C. 12
D. 13
find x if mA = 3x + 9 and mB = 8x – 4.
Over Lesson 10–4
A. 47.5°
B. 95°
C. 190°
D. 265°
The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it?
You used the Pythagorean Theorem to find side lengths of right triangles. (Lesson 8–2)
• Use properties of tangents.
• Solve problems involving circumscribed polygons.
• tangent
• point of tangency
• common tangent
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.
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.
A. 2 common tangents
B. 4 common tangents
C. 6 common tangents
D. no common tangents
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. 3 common tangents
C. 4 common tangents
D. no common tangents
B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.
Identify a Tangent
Test to see if ΔKLM is a right triangle.
?202 + 212 = 292 Pythagorean Theorem
841 = 841 Simplify.
Answer:
A.
B.
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
2 + 32x + 256 Multiply.
320 = 32x Simplify.
10 = x Divide each side by 32.
Answer: x = 10
A. 6
B. 8
C. 10
D. 12
Use Congruent Tangents to Find Measures
AC = BC Tangents from the same exteriorpoint 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
A. 5
B. 6
C. 7
D. 8
Find Measures in Circumscribed Polygons
Step 1 Find the missing measures.
Find Measures in Circumscribed Polygons
Step 2 Find the perimeter of ΔQRS.
Answer: So, the perimeter of ΔQRS is 36 cm.
= 10 + 2 + 8 + 6 + 10 or 36 cm
A. 42 cm
B. 44 cm
C. 48 cm
D. 56 cm