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Splash Screen. 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

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Lesson menu

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

Lesson Menu


5 minute check 1

A

B

C

D

A.

B.

C.

D.

5-Minute Check 1


5 minute check 2

A

B

C

D

A.

B.

C.

D.

5-Minute Check 2


5 minute check 3

A

B

C

D

A. STW

B. VWT

C. WVU

D. WRS

5-Minute Check 3


5 minute check 4

A

B

C

D

___

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

A. 6

B. 18

C. 24

D. 27

5-Minute Check 4


5 minute check 5

A

B

C

D

Find the magnitude and direction of for 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°

5-Minute Check 5


5 minute check 6

A

B

C

D

Which of the following transformations does not preserve length?

A. dilation

B. reflection

C. rotation

D. translation

5-Minute Check 6


Ngsss

MA.912.G.6.1Determine 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.

NGSSS


Then now

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.

Then/Now


Vocabulary

  • circumference

  • pi ()

  • inscribed

  • circumscribed

  • center

  • radius

  • chord

  • diameter

  • congruent circles

  • concentric circles

Vocabulary


Concept
Concept 6–2)


Example 1

Identify Segments in a Circle 6–2)

A. Name the circle and identify a radius.

Example 1


Example 11

Identify Segments in a Circle 6–2)

B. Identify a chord and a diameter of the circle.

Example 1


Example 12

A 6–2)

B

C

D

A.

B.

C.

D.

A. Name the circle and identify a radius.

Example 1


Example 13

A 6–2)

B

C

D

A.

B.

C.

D.

B. Which segment is not a chord?

Example 1


Concept1
Concept 6–2)


Example 2

If 6–2)RT = 21 cm, what is the length of QV?

RT is a diameter and QV is a radius.

Find Radius and Diameter

d = 2r Diameter Formula

21 = 2rd = 21

10.5 = r Simplify.

Answer:QV = 10.5 cm

Example 2


Example 21

A 6–2)

B

C

D

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

A. 12 cm

B. 13 cm

C. 16 cm

D. 26 cm

Example 2


Concept2
Concept 6–2)



Example 31

Since the diameter of is 16 units, 6–2)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

First, find ZY.

WZ + ZY = WY

5 + ZY = 8

ZY = 3

Next, find XY.

XZ + ZY = XY

11 + 3 = XY

14 = XY

Example 3


Example 32

Find Measures in Intersecting Circles 6–2)

Answer:XY = 14 units

Example 3


Example 33

A 6–2)

B

C

D

A. 3 in.

B. 5 in.

C. 7 in.

D. 9 in.

Example 3


Concept3
Concept 6–2)


Example 4

Find Circumference 6–2)

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 = dCircumference 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.

Example 4


Example 41

A 6–2)

B

C

D

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

Example 4


Example 5

Divide each side by . 6–2)

Find Diameter and Radius

Find the diameter and the radius of a circleto the nearest hundredth if the circumference of the circle is 65.4 feet.

Circumference Formula

Substitution

Use a calculator.

Example 5


Example 51

Find Diameter and Radius 6–2)

Radius Formula

Use a calculator.

Answer:d ≈ 20.82 ft; r ≈ 10.41 ft

Example 5


Example 52

A 6–2)

B

C

D

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

Example 5


Example 6

Read the Test Item 6–2)

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

Example 6


Example 61

Solve the Test Item 6–2)

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.

Example 6


Example 62

So the radius of the circle is 3. 6–2)

Circumference formula

Substitution

Answer: 6 units

Example 6


Example 63

A 6–2)

B

C

D

A.

B.

C.

D.

Example 6