Extra Practice BLM 7.1
7.1 Explore Polygons and Their Properties
Name: ____________________________________Date: _____________________________
1.
Classify each polygon as either regular or not regular. Explain your reasoning.
a)
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_________________________________
b)
_________________________________
_________________________________
c)
_________________________________
_________________________________
2.
Is the following figure convex or concave? Explain your choice.
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.
Name: ____________________________________Date: _____________________________
_________________________________
3.
What order of rotational symmetry do each of the pattern blocks have?
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Use these polygons for question 4 and 5.
A square
F parallelogram
B rectangle
G regular pentagon
C trapezoid
H isosceles trapezoid
D rhombus
I regular octagon
E isosceles triangle
J equilateral triangle
4.
.
Put the letter for each polygon in the Venn Diagram.
Name: ____________________________________Date: _____________________________
At Least One
Right Angle
At Least One Pair
of Parallel Sides
At Least One Pair of
Congruent Sides
5.
a)
Create a sorting rule for the Venn diagram.
b)
Classify the polygons according to your sorting rule.
Extra Practice BLM 7.2
7.2 Tessellations
.
Name: ____________________________________Date: _____________________________
1.
A tessellation has Schlafli notation {3,6,3,6}.
a)
What polygons are required to create this pattern?
______________________________
______________________________
b)
How many of these surround each point where vertices meet?
______________________________
______________________________
c)
Is this a semi-regular or a regular tessellation? Explain your thinking.
______________________________
______________________________
d)
2.
Draw the tessellation.
This is a {4,4,4,4} tessellation
a)
Explain how you can
replacing some squares with
using squares.
change it to a semi-regular tessellation by
octagons.
______________________________
______________________________
b)
Draw this semi-regular tessellation.
c)
Describe the semi-regular tessellation using Schlafli notation.
______________________________
3.
A tessellation has Schlafli notation {4,6,12}.
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a)
What polygons are required to create this pattern?
______________________________
______________________________
b)
How many of these surround each point where vertices meet?
______________________________
______________________________
c)
4.
Draw the tessellation.
Refer to the semi-regular tessellation in question 2 part b). Look at one of the squares.
a)
What transformation(s) will allow you to produce the other squares?
______________________________
______________________________
b)
Can the same transformation(s) be applied to produce the octagons from one octagon?
Explain.
______________________________
______________________________
c)
Is it possible to transform a square/octagon combination to produce the rest of the
tessellation? Explain why or why not.
______________________________
______________________________
______________________________
Extra Practice BLM 7.3
7.3 Regular Polyhedra
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Name: ____________________________________Date: _____________________________
1.
Which of the following are nets of a cube?
a)
b)
c)
d)
e)
2.
There are eleven possible nets of a cube. Can you produce the other seven missing from
question 1? Use Polydron® Pieces and draw your nets.
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Name: ____________________________________Date: _____________________________
3.
What regular polygons form the faces of each of the Platonic solids?
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_________________________________
_________________________________
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4.
a)
Sketch both nets for a regular tetrahedron.
b)
Why can you only make two nets?
______________________________
______________________________
______________________________
5.
Another name for a cube is a hexahedron. Explain why this name is a good description of a cube.
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6.
Connect four squares around a vertex. Are you able to build a solid? Explain why or why not.
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7.
You have been asked to design a package shaped like a Platonic solid for a new brand of
flavoured popcorn.
a)
Which platonic solid will you choose? Justify your choice.
______________________________
______________________________
b)
package.
Draw a net of your Platonic solid. Decorate it with your package design. Construct your
Extra Practice BLM 7.4
7.4 Semi-Regular Polyhedra
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Name: ____________________________________Date: _____________________________
1.
Build a polyhedron using octagons and equilateral triangles.
a)
What is the Schlafli notation for the polyhedron?
______________________________
b)
Count the faces, edges, and vertices.
______________________________
c)
Does Euler’s Formula apply to this polyhedron? Explain.
______________________________
______________________________
d)
2.
Unfold the polyhedron to produce a net. Draw the net.
Examine two different polyhedrons made of pentagons and equilateral triangles.
a)
Write the Schlafli notation for each polyhedron.
______________________________
______________________________
b)
Fill in the table.
Polyhedron
c)
Faces
Edges
Vertices
Does Euler’s Formula apply to these polyhedrons? Explain.
______________________________
______________________________
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Name: ____________________________________Date: _____________________________
d)
How are the polyhedrons:
• similar?
_________________________________
_________________________________
• different?
_________________________________
_________________________________
3.
Build three different polyhedrons using squares and equilateral triangles.
a)
Fill in the table to show the number of triangles and squares used for each polyhedron.
Polyhedron
b)
Triangles
Squares
Write the Schlafli notation for each polyhedron.
______________________________
______________________________
______________________________
c)
Unfold each polyhedron to produce a net. Draw the nets.
d)
How are the polyhedrons:
• similar?
______________________________
______________________________
• different?
______________________________
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______________________________
Chapter 7 Practice Test BLM 7PT
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Name: ____________________________________Date: _____________________________
Selected Response
Select the best answer.
1.
A
Which of the following is a concave octagon?
B
C
2.
3.
D
Which Schlafli
A
{4,4,6}
B
{4,8,8}
C
{4,6,6}
D
{4,4,8}
notation correctly describes this tessellation?
Which statement is never true?
A
Archimedean solids have faces that are more than one kind of regular polygon.
B
Archimedean solids do not have vertex regularity.
C
Archimedean solids are truncated Platonic solids.
D
Archimedean solids are also called semi-regular polyhedra.
Short Response
Provide a complete solution.
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Name: ____________________________________Date: _____________________________
4.
Use pattern blocks to show how you can construct each polygon. Draw diagrams to illustrate
your answers.
a)
an equilateral triangle using three pieces (show two ways)
b)
5.
a)
know.
an equilateral triangle using four pieces
Is this
tessellation regular or semi-regular? Explain how you
______________________________
______________________________
b)
What types of polygons and how many of each of them surround any point where
vertices meet?
______________________________
c)
Describe the tessellation using Schlafli notation.
______________________________
Extended Response
Provide a complete solution.
6.
Suppose you truncate the corners of a regular octahedron, while maintaining vertex regularity.
a)
What is the name of the polyhedron that results?
______________________________
b)
What types of polygons are the faces? How many of each are there?
______________________________
c)
Build the polyhedron using Polydron® pieces.
d)
Classify this as a Platonic solid, an Archimedean solid, or neither. Justify your answer.
______________________________
______________________________
e)
What is the Schlafli notation for this polyhedron?
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______________________________
Chapter 7 Review
BLM 7R
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Name: ____________________________________Date: _____________________________
1.
For each of the following polygons:
•
name it according to the number of sides
•
classify it as regular or not regular
•
classify it as convex or concave
•
identify the lines of symmetry
•
identify the order of rotational symmetry
a)
2.
b)
Draw a tessellation for each Schlaffi notation.
a) {3, 6, 3, 6}
3.
b) {4, 4, 4, 4}
A regular
hexagon and two equilateral triangles are joined as
•
vertex
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Name: ____________________________________Date: _____________________________
shown.
a)
What single regular polygon will just fit to fill the gap around the vertex shown? Explain
using words and a diagram.
______________________________
______________________________
b)
illustrate.
c)
4.
What combination of two or more polygons will fill the gap? Draw a diagram to
Show a different solution to part b).
Build the following net and fold the pieces to form a polyhedron.
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Name: ____________________________________Date: _____________________________
a)
Classify the polyhedron as a Platonic solid, an Archimedean solid, or neither.
______________________________
b)
Justify your answer to part a).
______________________________
______________________________
c)
Count the faces, edges, and vertices.
______________________________
______________________________
______________________________
d)
Does Euler’s Formula apply to this polyhedron? Justify your answer.
______________________________
______________________________
Chapter 7 Extra Practice Answer Key
Get Ready
1. a) a = 160º b) b = 64º c) c = 120º
2. a) similar b) congruent c) neither
3. a) 0, 2 b) 8, 8 c) 2, 2
4. a), b), c) Answers may vary.
7.1 Explore Polygons and Their Properties
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Name: ____________________________________Date: _____________________________
1. a) regular b), c) not regular
2. Concave. Some of the diagonals are outside of the figure.
3. triangle: 3; square: 4; rhombus: 2; trapezoid: 1; hexagon: 6
4. right circle: C; bottom circle: E, G, J; right and bottom inner circle: D, I, F, H; left, right, and bottom
inner circle: A, B
5. a), b) Answers may vary.
7.2 Tessellations
1. a) triangles and hexagons b) 2 triangles and 2 hexagons c) Semi-regular. There is more than one
polygon in the tessellation.
d)
2. a), b), c) Answers may vary.
3. a) squares, hexagons, and dodecagons b) 1 square, 1 hexagon, and 1 dodecagon
c)
4. a), b), c) Answers may vary.
7.3 Regular Polyhedra
1. a), c), d), and e)
2.
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Name: ____________________________________Date: _____________________________
3. tetrahedron: equilateral triangles; cube: squares; octahedron: equilateral triangles; dodecahedron:
regular pentagons; icosahedron: equilateral triangles
4. a)
b) Answers may vary.
5. “Hex” means six and a cube has six sides.
6. No. Four squares form a 360º angle around a vertex. They cannot form a solid because they are flat.
7. a), b) Answers may vary.
7.4 Semi-Regular Polyhedron
1. a) {3,8,8}b) 14 faces, 36 edges, 24 vertices c) Yes. 14 + 24 = 36 + 2 d) Nets may vary.
2. a) {3,5,3,5}, {3,3,3,3,5} b) icosidodecahedron: 32 faces, 60 edges, 30 vertices; snub dodecahedron: 92
faces, 150 edges, 60 vertices
c) Yes. Icosidodecahedron: 32 + 30 = 60 + 2; snub dodecahedron: 92 + 60 = 150 + 2.
d) Similar: both are made of pentagons and equilateral triangles. Different: they each have a different
Schlafli notation and a different number of faces, vertices, and edges.
3. a) cuboctahedron: 8 triangles, 6 squares; rhombicuboctahedron: 8 triangles, 18 squares; snub cube:
32 triangles, 6 squares b) {3,4,3,4}, {3,4,4,4}, {3,3,3,3,4} c) Nets may vary.
d) Similar: all three are made of triangles, and squares. Different: they each have a different Schlafli
notation and a different number of faces, vertices, and edges.
Review
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Name: ____________________________________Date: _____________________________
1. a) not regular convex isosceles trapezoid, 1 line of symmetry, order of rotational symmetry 1 b) not
regular concave 16-gon, 8 lines of symmetry, order of rotational symmetry of 8
2. a)
b) Answers may vary.
3. a) hexagon, trapezoid, or rhombus b), c) Answers may vary.
4. a) neither b) The polyhedron does not have vertex regularity.
c) 5 faces, 8 edges, and 5 vertices d) Yes. 5 + 5 = 8 + 2
Practice Test
1. C
2. B
3. B
4. a), b), c) Answers may vary.
5. a) Regular. It is made of one kind of polygon and has vertex regularity. b) 6 isosceles triangles c)
{3,3,3,3,3,3}
6. a) truncated octahedron b) 6 squares, 8 hexagons d) Archimedean solid. It is made of two kinds of
regular polygons and has vertex regularity. e) {4,6,6}
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