Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m 1.
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Over Lesson 10–4 A. A B. B C. C D. D 60 Refer to the figure. Find m1.
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Transcript of Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m 1.
Over Lesson 10–4
A. A
B. B
C. C
D. D
60
Refer to the figure. Find m1.
Over Lesson 10–4
A. A
B. B
C. C
D. D
20
Refer to the figure. Find m2.
Over Lesson 10–4
A. A
B. B
C. C
D. D
100
Refer to the figure. Find m4.
Over Lesson 10–4
A. A
B. B
C. C
D. D
11
find x if mA = 3x + 9 and mB = 8x – 4.
• Use properties of tangents.
• Solve problems involving circumscribed polygons.
In this lesson we will:
• 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. A
B. B
C. C
D. D
4 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. A
B. B
C. C
D. D
3 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:
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
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
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
