Five-Minute Check (over Chapter 9)
CCSS
Then/Now
New Vocabulary
Key Concept: Special Segments in a Circle
Example 1: Identify Segments in a Circle
Key Concept: Radius and Diameter Relationships
Example 2: Find Radius and Diameter
Key Concept: Circle Pairs
Example 3: Find Measures in Intersecting Circles
Key Concept: Circumference
Example 4: Real-World Example: Find Circumference
Example 5: Find Diameter and Radius
Example 6: Standardized Test Example: Circumference of Circumscribed
Polygon
Over Chapter 9
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Over Chapter 9
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Over Chapter 9
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Over Chapter 9
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Over Chapter 9
A. STW
B. VWT
C. WVU
D. WRS
Over Chapter 9
A. STW
B. VWT
C. WVU
D. WRS
Over Chapter 9
___
Find the length of the image of MN under a dilation
with scale factor k = 3 and MN = 9.
A. 6
B. 18
C. 24
D. 27
Over Chapter 9
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Find the length of the image of MN under a dilation
with scale factor k = 3 and MN = 9.
A. 6
B. 18
C. 24
D. 27
Over Chapter 9
Find the magnitude and direction of
A(4, 2) and B(–2, –1).
A. 2.2; 63.4°
B. 4.5; 243.4°
C. 6.7; 206.6°
D. 6.7; 26.6°
for
Over Chapter 9
Find the magnitude and direction of
A(4, 2) and B(–2, –1).
A. 2.2; 63.4°
B. 4.5; 243.4°
C. 6.7; 206.6°
D. 6.7; 26.6°
for
Over Chapter 9
Which of the following transformations does not
preserve length?
A. dilation
B. reflection
C. rotation
D. translation
Over Chapter 9
Which of the following transformations does not
preserve length?
A. dilation
B. reflection
C. rotation
D. translation
Content Standards
G.CO.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line,
distance along a line, and distance around a
circular arc.
G.C.1 Prove that all circles are similar.
Mathematical Practices
4 Model with mathematics.
1 Make sense of problems and persevere in
solving them.
You identified and used parts of
parallelograms.
• Identify and use parts of a circle.
• Solve problems involving the circumference
of a circle.
• circle
• concentric circles
• center
• circumference
• radius
• pi ()
• chord
• inscribed
• diameter
• circumscribed
Identify Segments in a Circle
A. Name the circle and identify a radius.
Identify Segments in a Circle
A. Name the circle and identify a radius.
Identify Segments in a Circle
B. Identify a chord and a diameter of the circle.
Identify Segments in a Circle
B. Identify a chord and a diameter of the circle.
A. Name the circle and identify a radius.
A.
B.
C.
D.
A. Name the circle and identify a radius.
A.
B.
C.
D.
B. Which segment is not a chord?
A.
B.
C.
D.
B. Which segment is not a chord?
A.
B.
C.
D.
Find Radius and Diameter
If RT = 21 cm, what is the length of QV?
RT is a diameter and QV is a
radius.
d = 2r
21 = 2r
10.5 = r
Answer:
Diameter Formula
d = 21
Simplify.
Find Radius and Diameter
If RT = 21 cm, what is the length of QV?
RT is a diameter and QV is a
radius.
d = 2r
21 = 2r
10.5 = r
Diameter Formula
d = 21
Simplify.
Answer: QV = 10.5 cm
If QS = 26 cm, what is the length of RV?
A. 12 cm
B. 13 cm
C. 16 cm
D. 26 cm
If QS = 26 cm, what is the length of RV?
A. 12 cm
B. 13 cm
C. 16 cm
D. 26 cm
Find Measures in Intersecting Circles
Find Measures in Intersecting Circles
Since the diameter of
is 16 units, WY = 8.
Similarly, the diameter of
is 22 units, so XZ = 11.
WZ is part of radius XZ and part of radius WY.
First, find ZY.
WZ + ZY = WY
5 + ZY = 8
ZY = 3
Next, find XY.
XZ + ZY = XY
11 + 3 = XY
14 = XY
Find Measures in Intersecting Circles
Answer:
Find Measures in Intersecting Circles
Answer: XY = 14 units
A. 3 in.
B. 5 in.
C. 7 in.
D. 9 in.
A. 3 in.
B. 5 in.
C. 7 in.
D. 9 in.
Find Circumference
CROP CIRCLES A series of crop circles was
discovered in Alberta, Canada, on September 4,
1999. The largest of the three circles had a radius of
30 feet. Find its circumference.
Since the radius is 30 feet, and d = 2r, the
diameter = 2(30) or 60 feet.
C = d
Answer:
Circumference formula
= (60)
Substitution
= 60
Simplify.
≈ 188.50
Use a calculator.
Find Circumference
CROP CIRCLES A series of crop circles was
discovered in Alberta, Canada, on September 4,
1999. The largest of the three circles had a radius of
30 feet. Find its circumference.
Since the radius is 30 feet, and d = 2r, the
diameter = 2(30) or 60 feet.
C = d
Circumference formula
= (60)
Substitution
= 60
Simplify.
≈ 188.50
Use a calculator.
Answer: The circumference of the crop circle is 60
feet or about 188.50 feet.
The Unisphere is a giant steel globe that sits in
Flushing Meadows-Corona Park in Queens,
New York. It has a diameter of 120 feet. Find its
circumference.
A. 377.0 feet
B. 392.5 feet
C. 408.3 feet
D. 422.1 feet
The Unisphere is a giant steel globe that sits in
Flushing Meadows-Corona Park in Queens,
New York. It has a diameter of 120 feet. Find its
circumference.
A. 377.0 feet
B. 392.5 feet
C. 408.3 feet
D. 422.1 feet
Find Diameter and Radius
Find the diameter and the radius of a circle to the
nearest hundredth if the circumference of the circle
is 65.4 feet.
Circumference Formula
Substitution
Divide each side by .
Use a calculator.
Find Diameter and Radius
Radius Formula
Use a calculator.
Answer:
Find Diameter and Radius
Radius Formula
Use a calculator.
Answer: d ≈ 20.82 ft; r ≈ 10.41 ft
Find the radius of a circle to the nearest hundredth
if its circumference is 16.8 meters.
A. 8.4 m
B. 5.35 m
C. 2.67 m
D. 16.8 m
Find the radius of a circle to the nearest hundredth
if its circumference is 16.8 meters.
A. 8.4 m
B. 5.35 m
C. 2.67 m
D. 16.8 m
Circumference of
Circumscribed Polygon
Read the Test Item
You need to find the diameter of the circle and use it to
calculate the circumference.
Circumference of
Circumscribed Polygon
Solve the Test Item
The radius of the circle is the same length as either leg
of the triangle. The legs of the triangle have equal
length. Call the length x.
Pythagorean Theorem
Substitution
Simplify.
Divide each side by 2.
Take the square root
of each side.
Circumference of
Circumscribed Polygon
So the radius of the circle is 3.
Circumference formula
Substitution
Answer:
Circumference of
Circumscribed Polygon
So the radius of the circle is 3.
Circumference formula
Substitution
Answer: 6 units
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B.
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B.
C.
D.