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1.
Chapter 11
Geometry and Measurement
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2.
Geometry and Measurement
11
Lesson 11-1 Geometry: Congruent
Lesson 11-2 Geometry: Symmetry
Lesson 11-3 Measurement: Perimeter
Lesson 11-4 Problem-Solving Strategy: Solve a
Simpler Problem
Lesson 11-5 Measurement: Area
Lesson 11-6 Problem-Solving Investigation:
Choose a Strategy
Lesson 11-7 Measurement: Area of Complex
Figures
3.
11-1 Geometry: Congruent
Five-Minute Check (over Chapter 10)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Geometry: Congruent
4.
11-1 Geometry: Congruent
• I will identify congruent figures.
• congruent
5.
11-1 Geometry: Congruent
Standard 4MG3.3 Identify congruent figures.
6.
11-1 Geometry: Congruent
Tell whether the figures are congruent.
The figures have the same size and shape.
Answer: Yes, the pentagons are congruent.
7.
11-1 Geometry: Congruent
Tell whether the figures are congruent.
A. Yes
B. No
8.
11-1 Geometry: Congruent
Tell whether the figures are congruent.
The figures are the same shape, but they are not
the same size.
Answer: No, the triangles are not congruent.
9.
11-1 Geometry: Congruent
Tell whether the figures are congruent.
A. Yes
B. No
10.
11-1 Geometry: Congruent
Determine whether the gardens are congruent.
Mr. Smith Mr. Bose
10 ft.
8 ft.
5 ft.
4 ft.
11.
11-1 Geometry: Congruent
The diagrams show that both classrooms have the
same shape. They are both rectangles.
Mr. Smith’s garden has a larger length and a larger
width. So, the gardens are not the same size.
Answer: Since the gardens have different sizes, they
are not congruent.
12.
11-1 Geometry: Congruent
Determine whether the windows are congruent.
3 ft.
3 ft.
5 ft.
6 ft.
A. Yes
B. No
13.
11-2 Geometry: Symmetry
Five-Minute Check (over Lesson 11-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
14.
11-2 Geometry: Symmetry
• I will identify figures that have bilateral and
rotational symmetry.
• line symmetry • bilateral symmetry
• line of symmetry • rotational symmetry
15.
11-2 Geometry: Symmetry
Standard 4MG3.4 Identify figures that have
bilateral and rotational symmetry.
16.
11-2 Geometry: Symmetry
Tell whether the figure has line symmetry. Then
tell how many lines of symmetry the figure has.
Answer: Yes; the figure has 1 line of symmetry.
17.
11-2 Geometry: Symmetry
Tell whether the figure has line symmetry. Then tell
how many lines of symmetry the figure has.
A. Yes; 1
B. Yes; 2
C. Yes; 4
D. No
18.
11-2 Geometry: Symmetry
Tell whether the figure has line symmetry. Then
tell how many lines of symmetry the figure has.
Answer: Yes; the figure has 2 lines of symmetry.
19.
11-2 Geometry: Symmetry
Tell whether the figure has line symmetry. Then tell
how many lines of symmetry the figure has.
A. Yes; 1
B. Yes; 2
C. Yes; 3
D. No
20.
11-2 Geometry: Symmetry
Tell whether the figure has rotational symmetry.
21.
11-2 Geometry: Symmetry
Answer: The figure has rotational symmetry because it
is the same after each rotation.
22.
11-2 Geometry: Symmetry
Tell whether the figure has rotational symmetry.
A. Yes
B. No
23.
11-3 Measurement: Perimeter
Five-Minute Check (over Lesson 11-2)
Main Idea and Vocabulary
California Standards
Key Concept: Perimeter of a Rectangle
Example 1
Example 2
24.
11-3 Measurement: Perimeter
• I will find the perimeter of a polygon.
• perimeter
25.
11-3 Measurement: Perimeter
Standard 4MG1.4 Understand and use formulas
to solve problems involving perimeters and
areas of rectangles and squares. Use those
formulas to find the areas of more complex figures
by dividing the figures into basic shapes.
26.
11-3 Measurement: Perimeter
Standard 4AF1.4 Use and interpret
formulas to answer questions about
quantities and their relationships.
28.
11-3 Measurement: Perimeter
Meli is creating a pen for her puppy. The picture
shows the layout for the pen. What is the perimeter
of the pen?
36 in.
60 in.
29.
11-3 Measurement: Perimeter
One Way: Use Addition
Add the measures of all of the sides of
the figure.
P = 36 + 36 + 60 + 60
P = 192
30.
11-3 Measurement: Perimeter
Another Way: Use Formula
Multiply the length and the width by 2.
Then add.
P = (2 × ) + (2 × w)
P = (2 × 60) + (2 × 36)
P = 120 + 72 or 192
Answer: So, the perimeter of the pen is 192 inches.
31.
11-3 Measurement: Perimeter
Surgie wants to build a fence for her yard. The
picture shows the layout of her fence around the
yard. What is the perimeter of the fence?
A. 46 ft.
B. 192 ft.
21 ft.
C. 525 ft.
D. 92 ft. 25 ft.
32.
11-3 Measurement: Perimeter
Find the perimeter of a square with a side of 7
centimeters.
There is more than one way to find the perimeter of
a square.
33.
11-3 Measurement: Perimeter
One Way: Use Addition
Add the measures of all of the sides of the
figure.
P=7+7+7+7
P = 28
34.
11-3 Measurement: Perimeter
Another Way: Use Formula
Multiply the length of one side by 4 because
there are 4 sides of equal length.
P = 4 × side length
P=4×7
P = 28
Answer: So, the perimeter of the square is 28.
35.
11-3 Measurement: Perimeter
Find the perimeter of a square with a side of 11
centimeters.
A. 11 cm
B. 15 cm
C. 44 cm
D. 55 cm
36.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Five-Minute Check (over Lesson 11-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
37.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
• I will solve problems by solving a simpler problem.
38.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Standard 4MR1.2 Determine when and how to
break a problem into simpler parts.
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.
39.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Pearl is painting a backdrop that is 30 feet
long and 12 feet wide for her school play. The
backdrop needs two coats of paint. She has
two cans of paint. Each can of paint covers
400 square feet of backdrop. Does Pearl have
enough paint?
40.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Understand
What facts do you know?
• The 30 foot by 12 foot backdrop needs two coats
of paint.
• Pearl has two cans of paint.
• Each can of paint covers 400 square feet of the
backdrop.
What do you need to find?
• Does Pearl have enough paint?
41.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Plan
Find how much paint is needed to paint the
backdrop twice. Then find the total area the two
cans of paint will cover and compare. You can
solve a simpler problem to find the answer.
42.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Solve
Find the area of one section of the backdrop.
10 × 12 = 120 square feet
To find the area of the entire backdrop, multiply the
area of one section of the backdrop by 3.
43.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Solve
So, the area of the backdrop equals 120 × 3 or
360 square feet.
Since the backdrop needs to be painted
twice, you need 360 + 360 or 720 square feet of
paint.
Answer: Since 720 < 800, there is enough paint.
44.
11-4 Problem-Solving Strategy: Solve a Simpler Problem
Check
The area of the backdrop is 30 × 12 or 360 square
feet. Two coats of paint would need to cover 720
square feet. Since Pearl has enough paint to cover
800 square feet, the answer is correct.
45.
11-5 Measurement: Area
Five-Minute Check (over Lesson 11-4)
Main Idea and Vocabulary
California Standards
Key Concept: Area of a Rectangle
Key Concept: Area of a Square
Example 1
Example 2
Perimeter and Area
46.
11-5 Measurement: Area
• I will find the area of rectangles and squares.
• area
• square units
47.
11-5 Measurement: Area
Standard 4MG1.4 Understand and use formulas
to solve problems involving perimeters and areas
of rectangles and squares. Use those formulas to
find the areas of more complex figures by dividing
the figures into basic shapes.
50.
11-5 Measurement: Area
Write a formula to find the area of the rectangle.
51.
11-5 Measurement: Area
One Way: Count the square units.
Make a rectangle 4 by 7 square units.
There are 28 square units.
52.
11-5 Measurement: Area
Another Way: Multiply
Multiply the length times the width to find the
area.
A = length × width
A= ×w
= 4 units × 7 units
= 28 square units
Answer: So, the area is 28 square units.
53.
11-5 Measurement: Area
What is the area of a rectangle with a length of 3 cm
and a width of 7 cm?
A. 10 cm2
B. 20 cm2
C. 21 cm2
D. 42 cm2
54.
11-5 Measurement: Area
What is the area of a square with sides that are 6
inches in length?
A = side × side Formula
A = 6 in. × 6 in. Replace s with 6.
A = 36 square inches Multiply.
Answer: So, the area of the square is 36 square
inches.
55.
11-5 Measurement: Area
What is the area of a square with sides that are
5 inches in length?
A. 5 square inches
B. 10 square inches
C. 20 square inches
D. 25 square inches
56.
11-6 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 11-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
57.
11-6 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
58.
11-6 Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing, and prioritizing information, and
observing patterns.
59.
11-6 Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.3 Solve problems involving
multiplication of multi-digit numbers by two-digit
numbers.
60.
11-6 Problem-Solving Investigation: Choose a Strategy
LYNN: It takes me 4 minutes to jog
one block in my neighborhood.
YOUR MISSION:
Find how long
it takes Lynn
to jog the
route in her
neighborhood
that is shown.
61.
11-6 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• It takes Lynn 4 minutes to jog one block.
• A map is given of her jogging route.
What do you need to find?
• How many minutes does it take her to
jog the route shown?
62.
11-6 Problem-Solving Investigation: Choose a Strategy
Plan
You can use the four-step plan and number
sentences to solve the problem.
63.
11-6 Problem-Solving Investigation: Choose a Strategy
Solve
First find the total number of blocks Lynn jogs.
Use the information given to find any measures
that are missing.
2 + 2 + 2 + 2 + 4 + 4 = 16
So, she jogs 16 blocks.
64.
11-6 Problem-Solving Investigation: Choose a Strategy
Solve
Use number sentences to find 4 minutes × 16
blocks.
Answer: So, Lynn jogs for 64 minutes.
65.
11-6 Problem-Solving Investigation: Choose a Strategy
Check
To check your work estimate an answer:
4 × 20 = 80. Since 80 is close to 64, the
answer is correct.
66.
11-7 Measurement: Area of Complex Figures
Five-Minute Check (over Lesson 11-6)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
67.
11-7 Measurement: Area of Complex Figures
• I will find the area of complex figures.
• complex figure
68.
11-7 Measurement: Area of Complex Figures
Standard 4MG1.4 Understand and use formulas
to solve problems involving perimeters and areas
of rectangles and squares. Use those formulas
to find the areas of more complex figures by
dividing the figures into basic shapes.
69.
11-7 Measurement: Area of Complex Figures
Find the area of the baseball stands.
Step 1 Break up the figure into smaller parts. The
figure is already broken up into two rectangles
that are easy to work with.
70.
11-7 Measurement: Area of Complex Figures
Step 2 Find the area of each part.
Horizontal Rectangle
A = length × width
A = 10 ft × 4 ft
A = 40 square feet
71.
11-7 Measurement: Area of Complex Figures
Vertical Rectangle
A = length × width
A = 14 ft × 4 ft
A = 56 square feet
72.
11-7 Measurement: Area of Complex Figures
Step 3 Add the areas.
40 square feet + 56 square feet = 96 square feet.
Answer: The area of the baseball stands is 96
square feet.
73.
11-7 Measurement: Area of Complex Figures
Find the area of the figure.
A. 97 square inches
B. 132 square inches
C. 127 square inches
D. 39 square inches
74.
11-7 Measurement: Area of Complex Figures
Find the area of the complex figure.
Step 1 Break up the figure into smaller parts. Look
for rectangles and squares. This figure can
be broken up into 1 rectangle and 2 squares.
75.
11-7 Measurement: Area of Complex Figures
Step 2 Find the area of each part.
Rectangle
A = length × width
A = 9 in. × 2 in.
A = 18 square inches
76.
11-7 Measurement: Area of Complex Figures
Square
A = side × side
A = 2 in. × 2 in.
A = 4 square inches
77.
11-7 Measurement: Area of Complex Figures
Step 3 Add the areas.
18 square feet + 4 square feet + 4 square feet
= 26 square feet
Answer: So, the area is 26 square feet.
78.
11-7 Measurement: Area of Complex Figures
Find the area of the complex figure.
A. 26 square C. 9 square
centimeters centimeters
B. 14 square D. 6 square
centimeters centimeters
79.
Geometry and Measurement
11
Five-Minute Checks
Geometry: Congruent
Perimeter and Area
81.
Geometry and Measurement
11
(over Chapter 10)
If a circle has a radius of 4 meters, what is the
length of the diameter?
A. 2 meters
B. 4 meters
C. 8 meters
D. 16 meters
82.
Geometry and Measurement
11
(over Chapter 10)
If a circle has a diameter of 12 inches, what is the
radius?
A. 2 inches
B. 6 inches
C. 12 inches
D. 24 inches
83.
Geometry and Measurement
11
(over Lesson 11-1)
Tell whether the figures are congruent.
A. Yes
B. No
84.
Geometry and Measurement
11
(over Lesson 11-1)
Tell whether the figures are congruent.
A. Yes
B. No
85.
Geometry and Measurement
11
(over Lesson 11-1)
Tell whether the figures are congruent.
A. Yes
B. No
86.
Geometry and Measurement
11
(over Lesson 11-1)
Tell whether the figures are congruent.
A. Yes
B. No
87.
Geometry and Measurement
11
(over Lesson 11-2)
Tell whether the figure has line symmetry. Then tell
how many lines of symmetry the figure has.
A. yes, 4
B. no, 0
C. yes, 1
D. yes, 2
88.
Geometry and Measurement
11
(over Lesson 11-2)
Tell whether the figure has line symmetry. Then tell
how many lines of symmetry the figure has.
A. yes, 1
B. yes, 2
C. no, 0
D. yes, 0
89.
Geometry and Measurement
11
(over Lesson 11-2)
Tell whether the figure has rotational symmetry.
A. yes
B. no
90.
Geometry and Measurement
11
(over Lesson 11-2)
Tell whether the figure has rotational symmetry.
A. yes
B. no
91.
Geometry and Measurement
11
(over Lesson 11-3)
Find the perimeter of a rectangle that is 12 feet long
and 3 feet wide.
A. 27 feet
B. 15 feet
C. 30 feet
D. 18 feet
92.
Geometry and Measurement
11
(over Lesson 11-3)
Find the perimeter of a square that is 9 yards on
one side.
A. 9 yards
B. 18 yards
C. 27 yards
D. 36 yards
93.
Geometry and Measurement
11
(over Lesson 11-4)
Solve. Lavanya buys a 5 pound watermelon for 41¢
per pound. Sabrina buys an 8 pound watermelon
for 25¢ per pound. Who spends more money, and
how much more?
A. Sabrina spends more money; $0.05
B. Lavanya spends more money; $0.05
C. Lavanya spends more money; $0.03
D. Lavanya spends more money; $0.16
94.
Geometry and Measurement
11
(over Lesson 11-5)
Find the area of a rectangle that is 3 inches by
7 inches.
A. 21 square inches
B. 10 inches
C. 21 inches
D. 10 square inches
95.
Geometry and Measurement
11
(over Lesson 11-5)
Find the area of a rectangle that is 2 cm by 8 cm.
A. 20 square centimeters
B. 10 square centimeters
C. 16 square centimeters
D. 18 square centimeters
96.
Geometry and Measurement
11
(over Lesson 11-5)
Find the area of a square that has sides of 5 yards.
A. 20 yards
B. 25 square yards
C. 20 square yards
D. 10 square yards
97.
Geometry and Measurement
11
(over Lesson 11-5)
Find the area of a square with 9 feet per side.
A. 18 square feet
B. 36 square feet
C. 72 square feet
D. 81 square feet
98.
Geometry and Measurement
11
(over Lesson 11-6)
Solve. On weekdays, a restaurant serves 25
customers for lunch and 50 for dinner. On Saturday
and Sunday, the number of customers doubles.
Find the number of customers the restaurant
serves in one week.
A. 375 customers
B. 525 customers
C. 675 customers
D. 1,050 customers
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