Five-Minute Check (over Chapter 9)

NGSSS

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

Over Chapter 9

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A. STW

B. VWT

C. WVU

D. WRS

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A. 6

B. 18

C. 24

D. 27

Find the length of the image of MN under a dilation with scale factor r = –3 and MN = 9.

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Over Chapter 9

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B. B

C. C

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A. 2.2; 63.4°

B. 4.5; 243.4°

C. 6.7; 206.6°

D. 6.7; 26.6°

Find the magnitude and direction of for A(4, 2) and B(–2, –1).

Over Chapter 9

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B. B

C. C

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A. dilation

B. reflection

C. rotation

D. translation

Which of the following transformations does not preserve length?

MA.912.G.6.1 Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons.

MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

Also addresses MA.912.G.6.5.

You identified and used parts of parallelograms. (Lesson 6–2)

• Identify and use parts of a circle.

• Solve problems involving the circumference of a circle.

• circle

• center

• radius

• chord

• diameter

• congruent circles

• concentric circles

• circumference

• pi ()

• inscribed

• circumscribed

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.

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B. B

C. C

D. D A B C D

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A. Name the circle and identify a radius.

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B. B

C. C

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B. Which segment is not a chord?

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B.

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D.

Find Radius and Diameter

Answer: QV = 10.5 cm

d = 2r Diameter Formula

21 = 2r d = 21

10.5 = r Simplify.

If RT = 21 cm, what is the length of QV?

RT is a diameter and QV is a radius.

A. A

B. B

C. C

D. D A B C D

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A. 12 cm

B. 13 cm

C. 16 cm

D. 26 cm

If QS = 26 cm, what is the length of RV?

Find Measures in Intersecting Circles

Find Measures in Intersecting Circles

First, find ZY.

WZ + ZY = WY

5 + ZY = 8

ZY = 3

Next, find XY.

XZ + ZY = XY

11 + 3 = XY

14 = XY

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.

Find Measures in Intersecting Circles

Answer: XY = 14 units

A. A

B. B

C. C

D. D A B C D

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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 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.

A. A

B. B

C. C

D. D A B C D

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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.

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

Use a calculator.

Divide each side by .

Find Diameter and Radius

Answer: d ≈ 20.82 ft; r ≈ 10.41 ft

Radius Formula

Use a calculator.

A. A

B. B

C. C

D. D A B C D

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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.

Read the Test Item

You need to find the diameter of the circle and use it to calculate the circumference.

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

Divide each side by 2.

Simplify.

Take the square root of each side.

Answer: 6 units

So the radius of the circle is 3.

Circumference formula

Substitution

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C. C

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