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Geometry
oals
G
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Learn
• estimate, measure, and draw
angles using a protractor
• make and apply generalizations
about the sum of angles in
triangles and quadrilaterals
• make and apply generalizations
about diagonal properties of
quadrilaterals
• sort quadrilaterals according
to properties
• make and interpret orthographic
drawings
• create cross-sections from solids
• make generalizations about the
planes of symmetry of solids
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Key Words
protractor
Georgette and Graham found scraps of
wood cut from these pieces of lumber.
rhombi
Venn diagram
chevron
orthographic drawing
mat plan
cross-section
plane symmetry
• What figures do you see on the faces
of the scraps?
• Which scraps go with which pieces?
How do you know?
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L E S S O N
Investigating Angles
You will need a protractor.
Your teacher will give you a large copy of these angles.
fig: G6_A_03-01-01
➤ Estimate the measure of each angle.
Record your estimates.
Then, find each angle measure.
Record the angle measures.
➤ Find the sum of the angles in each pair.
a and b
c and d
e and f
What do you notice about the angles
in each pair?
S h o w and S h a r e
Share your work with a classmate.
How did you estimate the measure of
each angle?
Were your estimates reasonable? Explain.
How did you use the measures of angles
a and b to estimate the measures of
angles c and d?
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LESSON FOCUS
Estimate, measure, and draw angles.
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Recall that you can use a protractor to draw or measure angles.
On a protractor, the measures
go from 0° to 180° clockwise
and counterclockwise.
➤ To measure an angle using a protractor, follow these steps:
Step 1
Estimate if the angle is less than
or greater than 90°.
I think this angle
is less than 90°.
Step 2
Place the protractor on top of
the angle.
The vertex of the angle is at
the centre of the protractor.
One arm of the angle lines up with
the base line of the protractor.
Step 3
Start at 0° on the arm
along the base line.
Find where the other arm
of the angle meets the protractor.
Recall the estimate, then read
the appropriate measure.
This angle measures 60°, not 120°.
This angle is
less than 90°.
Unit 3 Lesson 1
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➤ Follow these steps to construct an angle that measures 145°.
Step 1
With a ruler, draw one arm of the angle.
Step 2
Place the protractor on top of the arm.
One end of the arm is at the centre
of the protractor.
The arm lines up with the base line
of the protractor.
Start at 0° on the arm along the base line.
Make a mark at 145° so the angle is
greater than 90°.
Step 3
Remove the protractor.
Join the mark to the end of the arm placed
at the centre of the protractor.
Label the angle with its measure of 145°.
➤ The angle on a straight line measures 180°.
1. What is the measure of each angle? Explain how you know.
a)
b)
c)
2. For each angle:
• Estimate the angle measure.
• Use a protractor to find the angle measure.
a)
d)
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b)
e)
c)
f)
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3. Use a ruler and a protractor.
Construct an angle with each measure.
a) 80°
b) 30°
c) 100°
d) 150°
e) 180°
f) 10°
4. Name 4 objects in your classroom that have:
a) an angle greater than 100°
b) an angle less than 60°
Use a protractor to check your answers.
5. Draw an angle you think measures 140°.
Use a protractor to check your angle measure.
How close was your angle to 140°?
6. Without using a protractor, draw an angle that is 90° greater
than each of these angles.
a)
b)
Measure each angle with a protractor to check.
Explain how you drew each angle.
7. A student measured this angle and said it measured 60°.
Do you agree? Explain.
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Number Strategies
Order the numbers in each
set from least to greatest.
Draw an angle.
Explain how to use a protractor to measure the angle.
ASSESSMENT FOCUS
Question 6
• 123 321, 121 232,
123 231, 113 321
• 4 432 344, 4 344 342,
4 242 444, 4 432 413
Unit 3 Lesson 1
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L E S S O N
Sum of the Angles in Triangles
and Quadrilaterals
You will need a ruler, scissors, and a protractor.
Your teacher will give you 2 copies with three different triangles.
➤ Cut out the acute triangle from one copy.
Tear off the 3 angles.
Place the vertices of the 3 angles together,
so adjacent sides touch.
What do you notice?
Repeat the activity with the right triangle
and the obtuse triangle.
What do you notice?
What can you say about the sum of the
angles in each triangle?
➤ Use the triangles from the other copy.
Measure each angle with a protractor and
label it with its measure.
Find the sum of the angles in each triangle.
Does this confirm your results from tearing
off the angles? Explain.
S h o w and S h a r e
Compare your results with those of another pair of classmates.
What can you say about the sum of angles in a triangle? Explain.
➤ We can show that the sum of the angles in a triangle
is the same for all triangles.
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LESSON FOCUS
Make and apply generalizations about the sums of angles in figures.
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We label the angles in 3 congruent triangles.
We arrange the triangles to make a tessellation.
The angles in each triangle are a, b, and c.
The tessellation shows that these three angles make a straight angle.
So, a + b + c = 180°
The sum of the angles in a triangle is 180°.
➤ We can divide any quadrilateral into 2 triangles.
Since the sum of the angles in a triangle is 180°,
the sum of the angles in a quadrilateral is 2 180° 360°.
1. Draw a large obtuse triangle on dot paper. Measure each angle.
Find the sum of the measures of the angles.
2. Determine the missing angle measure without measuring.
a)
b)
c)
d)
e)
f)
Unit 3 Lesson 2
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3. Find the measure of the third angle in each triangle.
Then, draw the triangle.
Explain how you found each measure.
a) A triangle with two angles measuring 65° and 55°
b) A triangle with two equal angles; each measures 45°
c) A right triangle with a 70° angle
d) An isosceles triangle with one angle measuring 120°
4. a) What do you know about each angle in a square? A rectangle?
b) How can you use your answer in part a to find the sum of
the angles in a square or a rectangle?
5. Jacques and Alicia hiked from their cottage to the river.
They turned and hiked to their Grandma’s cottage.
Through which angle should they turn to get back to their cottage? Explain.
110°
Jacques
and Alicia’s
cottage
50°
Grandma’s cottage
6. Draw a pentagon.
Draw diagonals from one vertex to divide the pentagon into triangles.
Find the sum of the angles in a pentagon.
Check your answer by measuring the angles.
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7. How can you use the
first diagram in Connect
to verify that the sum of
the angles in a
quadrilateral is 360°?
Mental Math
Estimate each quotient.
2343 99
Explain how you know the sum of the angles in
any triangle or quadrilateral.
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ASSESSMENT FOCUS
Question 3
5456 50
3620 60
8405 12
Unit 3 Lesson 2
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L E S S O N
Properties of Diagonals
of Quadrilaterals
A diagonal of a quadrilateral joins 2 opposite vertices.
You will need scissors, a ruler, and a protractor.
Your teacher will give you copies of rhombi.
The plural of rhombus
is rhombi.
➤ Cut out the rhombi.
Each partner works with 1 rhombus.
➤ Use a ruler to draw 2 diagonals.
Measure the diagonals.
What do you notice?
➤ Use your protractor to measure:
• the angles where the
diagonals meet
• the angles formed where each
diagonal meets a vertex
What do you notice?
S h o w and S h a r e
Share your results with another pair
of students.
How are your results the same?
How are they different?
Do you think these results will be true
for all rhombi? Explain.
LESSON FOCUS
Make and apply generalizations about diagonals of quadrilaterals.
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➤ The diagonals of a rhombus have these
properties:
• They are perpendicular.
• They bisect each other.
• They form 4 congruent right triangles.
• They lie on the 2 lines of symmetry of the rhombus.
• They bisect the angles of the rhombus.
➤ We can use the properties of
a diagonal of a rhombus
to find the measures of all angles
when we measure one angle.
A diagonal lies on a line of symmetry,
so b = 66°.
A diagonal divides the rhombus into
2 congruent isosceles triangles.
In each triangle, the two equal angles
add up to 180° 66° 114°.
So, each equal angle is 114° 2 57°.
So, a 57° 57° 114°‚ and c 114°
1. Here is a rhombus.
Find the measure of each unknown angle without using a protractor.
Explain your thinking.
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2. Use square dot paper.
Draw a large parallelogram.
a) Measure each diagonal.
Record your findings.
b) What are the measures of the angles
where the diagonals meet?
c) What are the measures of the angles
formed by a diagonal at each vertex?
d) What do you notice about the triangles
that are formed?
e) How many diagonals lie on lines of symmetry?
3. Use square dot paper.
Draw a kite.
Draw the diagonals.
What are the properties of the diagonals of a kite?
4. List the properties of the diagonals of a rhombus
that are the same as those of a kite.
List the properties that are different.
5. Use square dot paper.
Draw a trapezoid.
Draw the diagonals.
What are the properties of the diagonals
of a trapezoid?
6. Draw a line segment that is 8 cm long.
Use a Mira.
Draw a rhombus that has this segment
as one of its diagonals.
Explain how you drew the rhombus.
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Number Strategies
Find each quotient.
How can you use the properties of the
diagonals of a parallelogram to list the
properties of the diagonals of a square
and a rectangle? Include diagrams.
ASSESSMENT FOCUS
Question 2
1530 9
8575 25
6344 52
2136 12
Unit 3 Lesson 3
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L E S S O N
Sorting Quadrilaterals
Your teacher will give you a copy of a set of figure cards
and a set of property cards.
➤ Player A chooses a property card
and places it face up.
Player B looks through the figure cards.
She places each figure card with
the property shown around the
property card.
The players discuss whether each
figure chosen is appropriate and
whether there are any figures missing.
Players record the properties and figures.
➤ Player B chooses another
property card, placing it over the
previous property card.
Player A determines which figure cards
should be removed, and whether
any figure cards should be added.
Players discuss the appropriateness
of the chosen figure cards.
Players record the properties and figures.
S h o w and S h a r e
Discuss the strategies you used to choose figures
with another pair of students.
How were your strategies similar?
How were they different?
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LESSON FOCUS
Sort quadrilaterals according to their properties.
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Number Strategies
Round each number to the
nearest thousand and to the
nearest hundred thousand.
• 4 682 364
• 803 091 531
• 9 989 899
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➤ This table shows the properties of trapezoids, parallelograms, rhombi, and kites.
Name
Properties
Trapezoid
• 1 pair of parallel sides
Parallelogram
•
•
•
•
•
Rhombus
•
•
•
•
Kite
•
•
•
•
Example
2 pairs of parallel sides
opposite sides equal
opposite angles equal
diagonals that bisect each other
diagonals that form 2 pairs
of congruent triangles
all sides equal
opposite angles equal
2 pairs of parallel sides
diagonals that are perpendicular
bisectors
• diagonals that form 4 congruent
right triangles
• diagonals that lie on 2 lines
of symmetry
• diagonals that bisect the
angles of the rhombus
2 pairs of equal adjacent sides
1 pair of equal angles
diagonals that are perpendicular
diagonals that form 2 pairs of
congruent right triangles
• one diagonal that is bisected
• the other diagonal that lies on a
line of symmetry and bisects two
opposite angles of the kite
Math Link
Your World
Kites have been used for thousands of years. The earliest written
account of kite flying occurred about 200 B.C.E., when General Han
Hsin of the Han Dynasty flew a kite over the city walls. Han Hsin
used the kite to measure the length of a tunnel needed to reach the
enemy’s palace. Benjamin Franklin experimented with kites to
investigate atmospheric electricity. Guglielmo Marconi launched
transatlantic wireless communication with the help of a kite.
Unit 3 Lesson 4
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➤ We can use a Venn diagram to sort these quadrilaterals:
Parallelogram
Rhombus
The properties are:
• Diagonals are perpendicular.
Trapezoid
• Diagonals bisect each other.
Diagonals bisect each other
Diagonals are perpendicular
A trapezoid
has neither
property.
A kite has
diagonals that are
perpendicular.
Kite
A rhombus has diagonals
that are perpendicular
and bisect each other.
1. Copy this Venn diagram.
A parallelogram
has diagonals that
bisect each other.
Has 4 right angles
Has 4 congruent sides
a) Sort these quadrilaterals: trapezoid,
parallelogram, rectangle, square,
rhombus, and kite.
b) Which quadrilateral has all 3 properties?
Where is this quadrilateral on the
Venn diagram?
Has at least 1 pair of parallel sides
2. Draw a Venn Diagram, similar to that in question 1.
Choose 3 different properties.
a) Sort these quadrilaterals: trapezoid, parallelogram,
rectangle, square, rhombus, and kite.
b) Does any quadrilateral have all 3 properties? How do you know?
3. Name the quadrilateral. It has:
•
•
•
•
86
opposite angles equal
diagonals that are perpendicular bisectors of each other
diagonals that form four congruent right triangles
2 lines of symmetry
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4. Name the quadrilateral. It has:
• diagonals that are perpendicular and form
two pairs of congruent right triangles
• one diagonal that bisects the other
• one line of symmetry
5. Copy this table. Fill in each blank with Yes or No.
Type of
Quadrilateral
Do the diagonals
bisect each other?
Are the diagonals
perpendicular?
Do the diagonals
form two pairs of
congruent triangles?
Rectangle
Square
Parallelogram
Rhombus
Trapezoid
Kite
6. Use a geoboard and geobands.
a) Make quadrilaterals with each property:
• two obtuse angles
• two acute angles
• exactly one right angle
• diagonals that are perpendicular
Draw your quadrilaterals on square dot paper.
b) How many different quadrilaterals did you make for each property?
Name each quadrilateral if you can.
7. Is it possible for a quadrilateral to have:
• more than 2 obtuse angles?
• opposite angles equal and no lines of symmetry?
Use words and pictures to explain.
8. A chevron is a concave kite.
a) Draw a chevron on dot paper.
Make sure adjacent sides are equal.
b) What do you have to do to the diagonals so that the
properties of the diagonals of a kite apply to the chevron?
How can you use geometric properties to sort quadrilaterals?
Use words and pictures to explain.
ASSESSMENT FOCUS
Question 6
Unit 3 Lesson 4
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L E S S O N
Homework
1. All squares are quadrilaterals.
True
2. All rectangles are parallelograms.
True
3. All parallelograms are trapezoids.
False
4. The diagonals of rhombi are of equal length.
False
5. If a figure is a square, it is a trapezoid.
True
Look at Paolo’s quiz answers.
Are Paolo’s answers correct? Explain.
Create a list of five true or false statements based on the
properties of quadrilaterals.
Write your true or false answers on a separate page.
Strategies
for Success
• Get unstuck.
• Check and reflect.
• Focus on the
problem.
S h o w and S h a r e
Trade statements with a classmate.
Identify each of your classmate’s statements as true or false.
Discuss your answers with your classmate.
• Represent your
thinking.
• Select an answer.
• Do your best on
a test.
• Explain your answer.
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LESSON FOCUS
Check and reflect.
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Marg considered this statement: “All squares are rectangles.”
To find out if the statement was true or false,
Marg recorded these properties of a rectangle:
•
•
•
•
•
•
exactly four right angles
two pairs of parallel sides
opposite sides equal
two lines of symmetry
diagonals equal
diagonals that form 2 pairs of congruent triangles
Marg looked at the list.
She placed a checkmark beside each property
that applied to a square.
She concluded that all the properties applied to a square.
So, the statement that all squares are rectangles is true.
1. Check each statement.
Is it true or false? Explain.
a) All rhombi are parallelograms.
b) All parallelograms are rectangles.
c) All squares are rhombi.
d) All parallelograms have equal diagonals.
Why is it important to always check your solution?
Unit 3 Lesson 5
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L E S S O N
Orthographic Drawings
Orthographic drawings are 2-D views of a 3-D object.
The views may be from the top, left, front, right, or back.
A mat plan is a top view that indicates the height of the cubes in the object.
The mat plan, below, represents the object on the right.
You will need Snap Cubes,
grid paper, and a ruler.
➤ Build an object using Snap Cubes.
On grid paper, draw a mat plan
of your object.
Hide the object.
➤ Trade mat plans with a classmate.
Build the object shown on your
classmate’s mat plan.
➤ Compare your object with the
object your classmate hid.
Are the objects the same? Explain.
S h o w and S h a r e
Use square dot paper.
Work together to draw as many different views of your object as possible.
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LESSON FOCUS
Make and interpret orthographic drawings.
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The orthographic views below represent this object.
To draw different views, it may be helpful
to use a building mat.
Place the object on the building mat.
Move the mat to draw each view.
The left and right of
the object are relative
to the front.
You will need Snap Cubes and grid paper. Use a building mat when it helps.
1. Use 5 Snap Cubes to build an object.
Draw the top, front, left, right, and back orthographic views.
Label each view.
2. Use Snap Cubes to build each object.
Draw a mat plan for each object.
Draw 5 orthographic views of each object.
a)
b)
Unit 3 Lesson 6
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3. Use Snap Cubes to build the object shown in each mat plan.
a)
b)
Draw the front, left, and right views of each object.
4. Look at the object below.
Which orthographic view represents the left view of the object?
Explain how you know.
5. Use Snap Cubes to build an object that has
these orthographic views.
Draw the left and back views of the object.
Explain how you built the object.
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Number Strategies
Can you build an object that has
different front and back views?
If your answer is yes, build the object
and sketch all 5 views.
If your answer is no, explain why you
cannot build the object.
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ASSESSMENT FOCUS
Question 5
Write 4 different numbers
that have a remainder of 3
when divided by 5.
How did you find the
numbers?
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Animator
ld of W
ork
Wor
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An animator uses artistic talent and sophisticated graphics software
to make movie scenes. But while the software may be sophisticated,
basic geometry is at its core.
Every movement of an object within an animated scene involves
one or more transformations. The animator chooses direction and
speed, and the software performs the transformations to match.
Animators continually adjust their instructions to make a scene more
realistic or exciting. New “routines” are stored and shared with the
other animators working on the project. Although everything
appears three-dimensional, calculations are done using
two-dimensional transformations with sizing changes.
Computer animators can recreate details that
would be impossible to get on film alone.
Sometimes, they can make the unbelievable
seem real.
Unit 3
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L E S S O N
Cross-Sections of Solids
You will need Plasticine and dental floss.
➤ Use the Plasticine to make four cones.
Place the cones with their bases on
the table.
Suppose you were to cut the cone
in each of these ways:
• horizontally
• vertically through its vertex
• slanting
• vertically, but not through its vertex
Sketch the figure you predict you
would see after each cut.
➤ Use the dental floss to cut the cones.
Record your findings.
S h o w and S h a r e
Compare your results with those of another pair
of students. How are the results the same?
How are they different?
Math Link
Science
Magnetic resonance imaging (MRI)
is a scan that generates crosssectional images of the brain or
other organs or body structures.
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LESSON FOCUS
Describe and represent various cross-sections of solids.
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A cross-section is the 2-D face produced when a cut is made
through a 3-D object.
➤ These pictures show the cross-sections of a pentagonal prism.
Vertically
Horizontally
Slanting
➤ These pictures show the cross-sections of a cylinder.
Parallel to the base
Vertically
Slanting
➤ These pictures show the cross-sections of a square pyramid.
Parallel to the base
Vertically through the vertex
Vertically not through the vertex
Slanting
You will need Plasticine and dental floss for question 3.
1. Name 2 figures found on the cross-sections of each solid.
a) cube
b) triangular prism
c) square pyramid
d) tetrahedron
A tetrahedron
is a triangular pyramid
with 4 congruent
faces.
Unit 3 Lesson 7
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2. Describe how a hexagonal prism could be cut to produce
each cross-section.
a) a hexagon
b) a rectangle
3. Use Plasticine to make 4 triangular prisms.
a) Sketch the figures you predict you would see on each cross-section.
The prism is cut:
i) parallel to its base
ii) parallel to one of its rectangular faces
iii) slanting toward its base
iv) slanting toward a rectangular face
b) Use dental floss to cut the prism to check your answers
to part a. Record your findings.
4. A student said:
Cutting off a vertex from
any prism always produces a
triangular cross-section.
a) Is this statement true? Explain.
b) Is this statement true for pyramids? How do you know?
5. Explain how a square pyramid could be cut to produce
each cross-section.
a) a triangle
b) a rectangle
c) a trapezoid
6. Which 3-D solids have a cross-section that is an isosceles triangle?
Use words and pictures to explain.
7. Are circles and ovals cross-sections of any
prisms or pyramids?
Use words and pictures to explain.
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Mental Math
Which cross-sections are easier to visualize
than others?
Use words and pictures to explain.
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ASSESSMENT FOCUS
Question 4
Which is greater:
25% of $30 or 20% of $35?
Unit 3 Lesson 7
Unit 3 Lesson x
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L E S S O N
Planes of Symmetry
You will need Plasticine, dental floss, and a ruler.
➤ Use Plasticine to make a cube.
➤ Use dental floss to cut the cube into
2 congruent parts.
➤ How many different ways can you cut
the cube to make 2 congruent parts?
➤ Sketch each cut on a labelled view of the cube.
S h o w and S h a r e
Compare your findings with those of
another pair of students.
Did you find all the different ways to
cut the cube? Explain.
➤ A figure may have one or more lines of symmetry.
This rectangle has
2 lines of symmetry.
➤ Three-dimensional objects may also have symmetry.
A solid has plane symmetry if a plane can divide the solid
into 2 parts so that one part is the mirror image of the other.
LESSON FOCUS
Make generalizations about the planes of symmetry of 3-D solids.
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➤ A rectangular prism has 3 planes of reflective symmetry, as shown below.
The lines of symmetry of each rectangle lie on the planes of symmetry
of the prism.
➤ A square pyramid has 4 planes of symmetry.
Two vertical planes cut through
the midpoints of opposite sides.
Each plane makes 2 congruent
triangular faces.
Two vertical planes cut through
the diagonals of the base.
Each plane makes 2 congruent
triangular faces.
You will need Plasticine for questions 1 and 7,
and Snap Cubes for question 3.
1. Use Plasticine to make a square prism.
Use dental floss to cut the prism along a plane of symmetry.
a) Sketch the cross-section.
b) How many planes of symmetry does the prism have?
2. How many planes of symmetry does each object have?
a)
b)
c)
3. Use 10 Snap Cubes.
Make an object that has:
a) exactly one plane of symmetry
b) exactly two planes of symmetry
c) more than two planes of symmetry
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4. a) Compare the numbers of planes of symmetry
of a square prism and a rectangular prism.
Which prism has more planes of symmetry?
Explain.
b) Does a cube have more or fewer planes
of symmetry than each prism in part a?
Explain.
5. Look at this vase.
How many planes of symmetry
does the vase have?
Explain how you know.
6. How are the planes of symmetry
of a cone and a cylinder related? Explain.
7. Use Plasticine and dental floss when you need to.
a) How many planes of symmetry does a rectangular pyramid have?
b) How many lines of symmetry does a rectangle have?
c) Repeat parts a and b for a pyramid with a regular pentagon
as its base.
d) Use the results of parts a, b, and c above, question 1, and question 2c.
What conclusions can you make about the planes of symmetry
of a pyramid and the lines of symmetry of its base?
ay
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Ev
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b
Num
Number Strategies
Find the common factors of
the numbers in each pair.
Do all prisms have at least one plane of symmetry?
Use words and pictures to explain.
ASSESSMENT FOCUS
Question 4
40, 72
45, 63
50, 80
55, 132
Unit 3 Lesson 8
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Show What You Know
LESSON
1
1. Owen says he can make an angle smaller by making
the arms shorter.
Do you agree? Why or why not?
2. a) Use a protractor to draw a 40° angle.
b) Do not use a protractor.
Draw an angle that is 90° greater.
c) Use a protractor to check the angle in part b.
3. Fold a piece of paper to make a 45° angle.
What other angle have you made at the same time?
Explain.
2
4. A quadrilateral has angles measuring 60°, 50°, and 120°.
What is the measure of the 4th angle?
How do you know?
3
5. A parallelogram has one 55° angle.
Sketch the parallelogram.
Explain how you can use the properties of a parallelogram
to find the measures of the other angles.
6. Sketch a kite and a rectangle.
List the properties of a kite that are the same as those
of a rectangle.
3
4
7. Use square dot paper.
Make a quadrilateral that has:
a) three acute angles
b) exactly one right angle
c) diagonals that bisect each other
Name each quadrilateral if you can.
8. Consider the statement,“If a figure is a rhombus, it is also a square.”
Is this statement true or false?
How do you know?
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LESSON
6
9. Use 8 Snap Cubes to create a solid.
Use grid paper to draw the top, front, back, left, and right views.
Label each view.
10. Use Snap Cubes to build an object that has the views shown.
Draw the back and left views.
7
11. How many different solids can you name that have these cross-sections?
a) square
b) rectangle
c) circle
Sketch each solid you name and show
the cross-section.
UN IT
8
12. Use Plasticine to make 4 trapezoidal prisms.
Learnin
a) Sketch the figure you predict you would
see on each cross-section.
The prism is cut:
i) parallel to its base
ii) parallel to one of its rectangular faces
iii) slanting toward its base
iv) slanting toward a rectangular face
b) Use dental floss to cut the prisms to check
your answers to part a. Record your findings.
✓
✓
✓
13. a) Use Plasticine to make a tetrahedron.
Use dental floss to find how many
planes of symmetry a tetrahedron has.
b) Which figures make up the cross-sections
of the planes of symmetry?
✓
✓
✓
✓
g Goals
estimate, measure, and draw
angles using a protractor
make and apply
generalizations about the sum
of angles in triangles and
quadrilaterals
make and apply
generalizations about diagonal
properties of quadrilaterals
sort quadrilaterals according
to properties
make and interpret
orthographic drawings
create cross-sections from
solids
make generalizations about
the planes of symmetry
of solids
Unit 3
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It’s a Slice
You will need:
• Plasticine
• dental floss
Use the Plasticine to make a prism, a pyramid, a cone,
a cylinder, and a sphere.
Part 1
Try to make each cross-section by cutting the solids in different ways.
• a hexagon
• an octagon
• a parallelogram that is not a rectangle
• a circle
• a square
• an equilateral triangle
• a rectangle that is not a square
• a triangle that
is not equilateral
• a pentagon
Record which figures
you were able
to create and how
you created them.
Which figures were
impossible to make?
Explain why.
What conclusions
might you make
about the kinds of
polygons that can
be made from the
cross-sections of a
prism? A pyramid?
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ist
C h e ck L
Part 2
Try to make cross-sections with two
or more of these properties by cutting the solids.
• a triangle with at least two 60° angles
• a figure with 4 lines of symmetry
• a figure with perpendicular diagonals
• a figure with diagonals that bisect each other
• a figure whose angle sum is 360°
• a figure with one pair of parallel sides
• a figure with 2 lines of symmetry
Your work should show
illustrations of your
cross-sections with
figures named
explanations for the
cross-sections that are
not possible
conclusions about the
cross-sections that
are possible
✓
✓
✓
Sketch and name the types of polygons you create.
Identify the properties from the list above.
How are the properties of quadrilaterals related to
the cross-sections and planes of symmetry of solids?
Use diagrams in your explanation.
Unit 3
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