Reflectional Symmetry in Cubes and Regular Tetrahedra
Worksheet 1
School Name
Mathematics
Worksheet 1
Reflectional Symmetry in Cubes and Regular Tetrahedra
Name:
Class：
(
)
Section 0: Revision on the reflectional symmetry in plane figures
1. Draw the mirror images of the following objects reflected in the thick black lines.
(a)
(b)
(c)
2. There are reflectional symmetries in some of the following figures.
reflectional symmetry in those figures.
Rectangle
(a)
Square
(b)
Rhombus
(d)
Isosceles triangle
(c)
Parallelogram
(e)
Draw all axes of the
Regular pentagon
(f)
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Reflectional Symmetry in Cubes and Regular Tetrahedra
Worksheet 1
Section 1: Mirror image of 3D figures
The following figures are formed by either cuboids or right circular cylinders and they were put
closely to the surface of the mirror. Draw the corresponding mirror images of the objects in
Questions 1–3.
e.g.
1.
3.
2.
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Reflectional Symmetry in Cubes and Regular Tetrahedra
Worksheet 1
Section 2: Planes of the reflectional symmetry of cubes
Part A:
1. First, fold the 3 nets of “semi-cube” in the “Symmetry in 3D Figures” Package to form
semi-cubes and then assemble them to form 3 cubes.
2.
Put the “silver-coated” paper in the middle of the following 3 cubes (Figures 1a, 1b and 1c) and
their respective positions are DCBA, SRQP and HGFE. Answer the following questions by
observing their mirror images.
Points A, B, C and D are
the mid-points of the edges.
C
G
R
H
S
D
B
F
Q
A
Figure 1a
P
E
Figure 1b
Figure 1c
(a) Which of the mirror image(s) is/are the same as the object(s) behind the mirror?
(b) With the answer in (a), guess which of the cutting method(s) associated with the above 3
figures may create planes of reflectional symmetry in cubes?
(c) Write the names of the planes of the reflectional symmetry in these cubes.
(d) With the answer in (a), guess which of the cutting method(s) may not create planes of
reflectional symmetry?
Explain your answer.
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Reflectional Symmetry in Cubes and Regular Tetrahedra
3.
In the following cubes, the dot on each edge is its mid-point. Sketch one plane of the
reflectional symmetry in each diagram.
The mid-point of the edge
A
B
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C
D
C
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A
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D
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C
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G
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G
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H
Worksheet 1
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H
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F
G
Page 4 of 6
Reflectional Symmetry in Cubes and Regular Tetrahedra
Worksheet 1
Part B: Conclusion
1. There are totally
planes of reflectional symmetry in a cube. These planes can be
categorized into two main types (See Table 1). Use the results in Part A to complete the table
below.
The cube is divided into two equal
Relation with the quantities of
Quantity
solids. The name of such solid is
vertices, edges and faces of the cube
Type 1
Type 2
Total
Table 1
Section 3: Plane of reflectional symmetry of regular tetrahedron
Part A:
1.
2.
First, fold the long white strip in the “Symmetry in 3D Figures” Package to form a regular
tetrahedron.
Put the “silver-coated paper” in the middle of the regular tetrahedron (i.e. CBA in Figure 2).
Observe the mirror image and then answer the following questions:
C
B
Figure 2
A
(a) What is the relation between the shape of the figure in front of the mirror and that behind the
mirror?
(b) Is there reflectional symmetry in a regular tetrahedron?
(c) With the answer in (a), guess whether this cutting method can create a plane of
reflectional symmetry in a regular tetrahedron?
Explain your answer.
Page 5 of 6
Reflectional Symmetry in Cubes and Regular Tetrahedra
3.
Worksheet 1
Given the following regular tetrahedral, sketch one plane of reflectional symmetry in each
figure.
A
A
A
D
D
D
A
C
A
B
C
A
C
B
B
D
D
D
B
B
B
C
C
C
Part B: Conclusion
1. There are totally
planes of reflectional symmetry in a regular tetrahedron. Use
the results in Part A to complete the table below.
2.
The regular tetrahedron is
divided into two equal solids.
The name of such solid is
Quantity
Relation with the quantities of vertices,
edges and faces of the regular
tetrahedron
One type
only
Table 2
The End
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