Chapter 10
Geometry
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10
Geometry
Lesson 10-1
Solid Figures
Lesson 10-2
Plane Figures
Lesson 10-3
Problem-Solving Strategy: Look
for a Pattern
Lesson 10-4
Lines, Line Segments, and Rays
Lesson 10-5
Angles
Lesson 10-6
Problem-Solving Investigation:
Choose a Strategy
Lesson 10-7
Triangles
Lesson 10-8
Quadrilaterals
Lesson 10-9
Parts of a Circle
10-1
Solid Figures
Five-Minute Check (over Chapter 9)
Main Idea and Vocabulary
California Standards
Key Concept: Solid Figures
Example 1: Identify Solid Objects
10-1
Solid Figures
• I will identify, describe, and classify solid figures,
and identify and draw nets.
• solid figure
• vertex
• face
• net
• edge
10-1
Solid Figures
Standard 4MG3.6 Visualize, describe, and make
models of geometric solids (e.g. prisms,
pyramids) in terms of the number and shape of
faces, edges, and vertices; interpret twodimensional representations of threedimensional objects; and draw patterns (of
faces) for a solid that, when cut and folded, will
make a model of the solid.
10-1
Solid Figures
10-1
Solid Figures
A paper towel roll represents a
figure. Identify the figure. Tell
how many faces, edges, and
vertices it has.
Answer: The paper towel roll is a cylinder. It has
2 faces, 0 edges, and 0 vertices.
10-1
Solid Figures
A tennis ball represents a figure.
Identify the figure. Tell how many
faces, edges, and vertices it has.
A. cone; 1 face, 1 edge, 0 vertices
B. cylinder; 2 faces, 1 edge, 0 vertices
C. sphere; 2 faces, 1 edge, 0 vertices
D. sphere; 0 faces, 0 edges, 0 vertices
10-2
Plane Figures
Five-Minute Check (over Lesson 10-1)
Main Idea and Vocabulary
California Standards
Key Concept: Polygons
Example 1: Identify a Polygon
Example 2: Identify a Polygon
Example 3: Identify a Polygon
10-2
Plane Figures
• I will identify, describe, and classify plane figures.
• plane figure
• quadrilateral
• polygon
• pentagon
• sides
• hexagon
• triangle
• octagon
10-2
Plane Figures
Standard 4MG3.0 Students demonstrate an
understanding of plane and solid geometric
objects and use this knowledge to show
relationships and solve problems.
10-2
Plane Figures
10-2
Plane Figures
Identify the polygon.
Answer: The shape has 8 sides, so the shape is an
octagon.
10-2
Plane Figures
Identify the polygon.
A. triangle
B. quadrilateral
C. pentagon
D. hexagon
10-2
Plane Figures
Tell whether the shape is a polygon.
The shape is a circle and is one curved line. It does
not have straight sides.
Answer: It is not a polygon.
10-2
Plane Figures
Tell whether the shape
is a polygon.
A. yes
B. no
10-2
Plane Figures
Tell whether the shape is a polygon.
The figure has 10 sides. The sides are all straight.
Answer: So, it is a polygon.
10-2
Plane Figures
Tell whether the shape
is a polygon.
A. yes
B. no
10-3
Problem-Solving Strategy: Look for a Pattern
Five-Minute Check (over Lesson 10-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
10-3
Problem-Solving Strategy: Look for a Pattern
• I will solve problems by looking for a pattern.
10-3
Problem-Solving Strategy: Look for a Pattern
Standard 4MR1.1 Analyze problems by identifying
relationships, distinguishing relevant from irrelevant
information, sequencing and prioritizing information,
and observing patterns.
10-3
Problem-Solving Strategy: Look for a Pattern
Standard 4MG3.0 Students demonstrate an
understanding of plane and solid geometric
objects and use this knowledge to show
relationships and solve problems.
10-3
Problem-Solving Strategy: Look for a Pattern
Amado is helping his dad put tile on a table top.
They are laying the tiles in a pattern. They have
run out of tiles and need to buy more. What color
tiles need to be purchased to complete the table?
10-3
Problem-Solving Strategy: Look for a Pattern
Understand
What facts do you know?
• You know the tiles form a pattern.
• You know they need to buy more tiles.
What do you need to find?
• Find the tile colors that need to be purchased.
10-3
Problem-Solving Strategy: Look for a Pattern
Plan
Look for a pattern. Then continue the pattern to
find the missing tiles.
10-3
Problem-Solving Strategy: Look for a Pattern
Solve
There are two rows of tiles and the tiles repeat
red, green, blue, and yellow.
10-3
Problem-Solving Strategy: Look for a Pattern
Solve
In the first row, the missing tiles are blue and
green. In the second row, the missing tiles are
red, blue and yellow.
Answer: So, Amado and his father need 2 blue,
1 green, 1 red, and 1 yellow tile.
10-3
Problem-Solving Strategy: Look for a Pattern
Check
Look back at the problem. The answer makes
sense for the facts given. So, the answer is correct.
10-4
Lines, Line Segments, and Rays
Five-Minute Check (over Lesson 10-3)
Main Idea and Vocabulary
California Standards
Key Concepts: Lines, Rays, Segments
Key Concepts: Types of Lines
Example 1: Identify Lines, Rays, or Line Segments
Example 2: Identify Lines, Rays, or Line Segments
Example 3: Describe Lines
10-4
Lines, Line Segments, and Rays
• I will identify, describe, and classify lines, line
segments, and rays.
•
•
•
•
line
ray
endpoint
line segment
• parallel
• intersecting
• perpendicular
10-4
Lines, Line Segments, and Rays
Standard 4MG3.1 Identify lines that are parallel
and perpendicular.
10-4
Lines, Line Segments, and Rays
10-4
Lines, Line Segments, and Rays
10-4
Lines, Line Segments, and Rays
10-4
Lines, Line Segments, and Rays
10-4
Lines, Line Segments, and Rays
Identify the figure.
N
M
This line has two endpoints and does not extend in
either direction.
Answer: line segment MN or MN
10-4
Lines, Line Segments, and Rays
Identify the figure.
A
A. line AB
B. line segment AB
C. ray AB
D. none of the above
B
10-4
Lines, Line Segments, and Rays
Identify the figure.
R
T
The figure has arrows on each end, so it extends in
opposite directions without ending.
Answer: line RT or RT
10-4
Lines, Line Segments, and Rays
Identify the figure.
G
A. line GH
B. line segment GH
C. ray GH
D. none of the above
H
10-4
Lines, Line Segments, and Rays
Describe the figure.
W
X
The figure shows line
WX and line YT. They are
Y
the same distance apart
everywhere and will never
cross. WX
YT.
Answer: WX and YT are parallel lines.
T
10-4
Lines, Line Segments, and Rays
Describe the figure.
M
O
P
A. parallel lines
B. intersecting lines
C. perpendicular lines
D. none of the above
N
10-5
Angles
Five-Minute Check (over Lesson 10-4)
Main Idea and Vocabulary
California Standards
Key Concept: Turns and Angles
Key Concept: Types of Angles
Example 1: Turns and Angles
Example 2: Classify an Angle
Example 3: Classify an Angle
10-5
Angles
• I will identify, describe, and classify angles.
• angle
• acute angle
• right angle
• obtuse angle
10-5
Angles
Standard 4MG3.5 Know the definitions of a right
angle, an acute angle, and an obtuse angle.
Understand that 90 , 180 , 270 , and 360 are
associated, respectively, with
turns.
,
,
, and full
10-5
Angles
10-5
Angles
10-5
Angles
Write how far the
minute hand has turned
in degrees and as a
fraction of a full turn.
Compare the angle shown on the clock to the angles
shown in the Key Concept: Turns and Angles box.
Answer: So, the angle shown on the clock is
180° or a
turn.
10-5
Angles
Write how far the minute hand has turned in
degrees and as a fraction of a full turn.
A. 90°;
turn
B. 180°;
turn
C. 270°;
turn
D. 360°; full turn
10-5
Angles
Classify the angle as acute, obtuse, or right.
The angle is greater than 90° and less than 180°.
Answer: So, it is an obtuse angle.
10-5
Angles
Classify the angle as acute,
obtuse, or right.
A. acute
B. obtuse
C. right
D. none of the above
10-5
Angles
Classify the angle as acute, obtuse, or right.
The angle is less than 90° and greater than 0°.
Answer: So, it is an acute angle.
10-5
Angles
Classify the angle as acute,
obtuse, or right.
A. acute
B. obtuse
C. right
D. none of the above
10-6
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 10-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
10-6
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
10-6
Problem-Solving Investigation: Choose a Strategy
Standard 4MR2.3 Use a variety of methods, such
as words, numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
10-6
Problem-Solving Investigation: Choose a Strategy
Standard 4MG3.0 Students demonstrate an
understanding of a plane and solid geometric
objects and use this knowledge to show
relationships and solve problems.
10-6
Problem-Solving Investigation: Choose a Strategy
ARTURO: I have the five puzzle
pieces shown. I need to form a
square using all of the pieces.
YOUR MISSION: Arrange the five
puzzle pieces to form a square.
10-6
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• You know there are five puzzle pieces.
What do you need to find?
• You need to find how to arrange the five
puzzle pieces to form a square.
10-6
Problem-Solving Investigation: Choose a Strategy
Plan
Use the act it out strategy. Trace the pieces and
cut them out of paper. Then arrange the polygons
in different ways to figure out how they will form a
square.
10-6
Problem-Solving Investigation: Choose a Strategy
Solve
Arrange the pieces in different ways until you
form a square.
10-6
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. The figure formed by
the pieces is a square because it is a rectangle
that has four equal sides. So, the answer is
correct.
10-7
Triangles
Five-Minute Check (over Lesson 10-6)
Main Idea and Vocabulary
California Standards
Key Concept: Classify Triangles by Sides
Key Concept: Classify Triangles by Angles
Example 1: Classify by Sides
Example 2: Classify by Sides and Angles
10-7
Triangles
• I will identify, describe, and classify triangles.
• isosceles triangle
• right triangle
• equilateral triangle
• acute triangle
• scalene triangle
• obtuse triangle
10-7
Triangles
Standard 4MG3.7 Know the definitions of
different triangles (e.g. equilateral, isosceles,
scalene) and identify their attributes.
10-7
Triangles
10-7
Triangles
10-7
Triangles
Classify the triangle.
Use isosceles,
equilateral, or
scalene.
Exactly 2 sides of the
triangle are the same
length.
6 in.
6 in.
3 in.
Answer: So, the triangle is isosceles.
10-7
Triangles
Classify the triangle. Use isosceles, equilateral,
or scalene.
3 cm
A. scalene
B. isosceles
C. equilateral
D. none of the above
3 cm
5 cm
10-7
Triangles
Classify the triangle. Use acute, right, or obtuse.
The triangle has one obtuse angle.
Answer: The triangle is obtuse.
10-7
Triangles
Classify the triangle. Use
acute, right, or obtuse.
10 ft
A. acute
B. right
C. obtuse
D. none of the above
8 ft
6 ft
10-8
Quadrilaterals
Five-Minute Check (over Lesson 10-7)
Main Idea and Vocabulary
California Standard
Key Concept: Quadrilaterals
Example 1: Classify a Quadrilateral
Example 2: Real-World Shape
Example 3: Classify a Quadrilateral
10-8
Quadrilaterals
• I will identify, describe, and classify quadrilaterals.
• rectangle
• parallelogram
• square
• trapezoid
• rhombus
10-8
Quadrilaterals
Standard 4MG3.8 Know the definitions of
different quadrilaterals (e.g. rhombus, square,
rectangle, parallelogram, trapezoid).
10-8
Quadrilaterals
10-8
Quadrilaterals
Classify the quadrilateral in as many ways as
possible.
The figure has 1 pair of parallel sides.
Answer: It can only be classified as a trapezoid.
10-8
Quadrilaterals
Classify the quadrilateral in
as many ways as possible.
A. trapezoid
B. parallelogram, rhombus, square
C. rectangle, square
D. parallelogram, rhombus
10-8
Quadrilaterals
Look at the picture. What shape is it?
A pan has 4 right angles with opposite sides
equal and parallel.
Answer: So, the picture is a rectangle.
10-8
Quadrilaterals
Look at the picture. What shape is it?
A. rectangle
B. square
C. rhombus
D. trapezoid
10-8
Quadrilaterals
Look at the picture. What shape is it?
All sides of the figure are equal and opposite
sides are parallel.
Answer: So, the figure is a rhombus.
10-8
Quadrilaterals
Look at the picture.
What shape is it?
A. parallelogram
B. square
C. rectangle
D. trapezoid
10-9
Parts of a Circle
Five-Minute Check (over Lesson 10-8)
Main Idea and Vocabulary
California Standard
Key Concept: Parts of a Circle
Example 1: Parts of a Circle
Example 2: Parts of a Circle
Example 3: Parts of a Circle
Example 4: Parts of a Circle
10-9
Parts of a Circle
• I will identify parts of a circle.
• circle
• diameter
• center
• radius
10-9
Parts of a Circle
Standard 4MG3.2 Identify the radius and
diameter of a circle.
10-9
Parts of a Circle
10-9
Parts of a Circle
Identify the part of the circle.
The line segment connects the center of the circle to
one point on the circle.
Answer: This is a radius.
10-9
Parts of a Circle
Identify the part of the circle.
A. radius
B. diameter
C. center
D. none of the above
10-9
Parts of a Circle
Identify the part of the circle.
The line segment connects two points on the circle
and goes through the center.
Answer: This is a diameter.
10-9
Parts of a Circle
Identify the part of the circle.
A. radius
B. diameter
C. center
D. none of the above
10-9
Parts of a Circle
Identify the part of
the circle that is
D
A
C
B
represented by CB.
F
CB is a line segment that connects the center of the
circle to a point on a circle.
Answer: So, CB is a radius.
10-9
Parts of a Circle
Identify the part of
the circle that is
D
A
C
represented by CD.
A. radius
B. diameter
C. center
D. none of the above
F
B
10-9
Parts of a Circle
Identify the part of
the circle that is
D
A
C
B
represented by AB.
F
AB is a line segment that connects two points on the
circle and goes through the center.
Answer: So, AB is a diameter.
10-9
Parts of a Circle
Identify the part of
the circle that is
D
A
C
represented by C.
A. radius
B. diameter
C. center
D. angle
F
B
10
Geometry
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10
Geometry
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10
Geometry
10
Geometry
10
Geometry
10
Geometry
10
Geometry
Lesson 10-1 (over Chapter 9)
Lesson 10-2 (over Lesson 10-1)
Lesson 10-3 (over Lesson 10-2)
Lesson 10-4 (over Lesson 10-3)
Lesson 10-5 (over Lesson 10-4)
Lesson 10-6 (over Lesson 10-5)
Lesson 10-7 (over Lesson 10-6)
Lesson 10-8 (over Lesson 10-7)
Lesson 10-9 (over Lesson 10-8)
10
Geometry
(over Chapter 9)
Divide. Use estimation to check.
5,575 ÷ 5
A. 1,111
B. 115
C. 1,115
D. 1,114
10
Geometry
(over Chapter 9)
Divide. Use estimation to check.
2,808 ÷ 8
A. 351
B. 401
C. 301
D. 315
10
Geometry
(over Chapter 9)
Divide. Use estimation to check.
57,125 ÷ 3
A. 18,041 R2
B. 18,041
C. 22,375
D. 19,041 R2
10
Geometry
(over Chapter 9)
Divide. Use estimation to check.
37,214 ÷ 7
A. 6,316 R2
B. 5,316 R2
C. 53 R4
D. 5,016 R2
10
Geometry
(over Lesson 10-1)
How many vertices does a sphere have?
A. 8
B. 4
C. 2
D. 0
10
Geometry
(over Lesson 10-1)
How many faces does a cylinder have?
A. 0
B. 2
C. 4
D. 8
10
Geometry
(over Lesson 10-1)
Describe a triangular pyramid.
A. It has a triangular base, 3 faces, 6
edges, 4 vertices.
B. It has a triangular base, 4 faces, 3
edges, 4 vertices.
C. It has a triangular base, 2 faces, 6
edges, 6 vertices.
D. It has a triangular base, 4 faces, 6
edges, 4 vertices.
10
Geometry
(over Lesson 10-1)
Name a solid figure that has 5 faces, 8 edges, and
5 vertices.
A. a triangular pyramid
B. a rectangular prism
C. a square pyramid
D. a cone
10
Geometry
(over Lesson 10-2)
Identify the polygon.
A. hexagon
B. triangle
C. pentagon
D. octagon
10
Geometry
(over Lesson 10-2)
Identify the polygon.
A. pentagon
B. octagon
C. quadrilateral
D. hexagon
10
Geometry
(over Lesson 10-2)
Identify the polygon.
A. pentagon
B. octagon
C. quadrilateral
D. triangle
10
Geometry
(over Lesson 10-2)
Identify the polygon.
A. hexagon
B. quadrilateral
C. octagon
D. pentagon
10
Geometry
(over Lesson 10-3)
Solve. Use the look for a pattern strategy. While
on vacation, Paul collected pinecones. On
Sunday, he collected 2. On Monday, he collected
9. On Tuesday, he collected 16. If this pattern
continues, how many pinecones will he collect
on Friday?
A. 23 pinecones
B. 30 pinecones
C. 37 pinecones
D. 44 pinecones
10
Geometry
(over Lesson 10-4)
Identify the figure below.
A. line CD
B. line segment CD
C. ray CD
D. parallel lines
C
D
10
Geometry
(over Lesson 10-4)
Identify the figure below.
A. line segment MN
M
B. ray MN
C. endpoint MN
D. line MN
N
10
Geometry
(over Lesson 10-4)
Identify the figure below.
A. ray RS
B. line segment RS
C. endpoint RS
D. line RS
R
S
10
Geometry
(over Lesson 10-5)
Classify the angle as right, acute, or obtuse.
A. obtuse
B. acute
C. right
10
Geometry
(over Lesson 10-5)
Classify the angle as right, acute, or obtuse.
A. obtuse
B. acute
C. right
10
Geometry
(over Lesson 10-5)
Classify the angle as right, acute, or obtuse.
A. obtuse
B. acute
C. right
10
Geometry
(over Lesson 10-5)
Classify the angle as right, acute, or obtuse.
A. obtuse
B. acute
C. right
10
Geometry
(over Lesson 10-6)
Identify 3 bills that total $25 using $1, $5, $10,
and $20 bills.
A. 1 $20 bill and 1 $5 bill
B. 5 $5 bills
C. 2 $10 bills and 1 $5 bill
D. 1 $10 bill and 3 $5 bills
10
Geometry
(over Lesson 10-6)
A number is multiplied by 3, then 5 is added to the
product. The result is 23. What was the original
number?
A. 6
B. 8
C. 15
D. 11
10
Geometry
(over Lesson 10-7)
Identify each triangle.
A. isosceles acute
B. scalene right
C. isosceles obtuse
D. equilateral acute
10
Geometry
(over Lesson 10-7)
Identify each triangle.
A. equilateral acute
6 cm
3 cm
B. scalene acute
C. scalene right
D. isosceles obtuse
4 cm
10
Geometry
(over Lesson 10-7)
Identify each triangle.
A. equilateral right
B. scalene acute
C. isosceles acute
D. equilateral acute
10
Geometry
(over Lesson 10-8)
Name a quadrilateral that has opposite sides
parallel and 4 right angles.
A. rhombus
B. trapezoid
C. rectangle
D. triangle
10
Geometry
(over Lesson 10-8)
Name a quadrilateral that has exactly 1 pair of
parallel sides.
A. square
B. rhombus
C. parallelogram
D. trapezoid
10
Geometry
(over Lesson 10-8)
Identify the quadrilateral.
A. trapezoid
B. rhombus
C. square
D. parallelogram
10
Geometry
(over Lesson 10-8)
Identify the quadrilateral.
A. square
B. rhombus
C. trapezoid
D. rectangle
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