Planes of Symmetry within a cube or cuboid
This demonstration allows you to view in turn the different planes of symmetry within a
cube. The demonstration should lead to a debate about whether each of these planes are in
fact planes of symmetry and whether or not any are missing. Students may well need to use
3D models to check some of the diagonal planes. Do they remain planes of symmetry if the
solid is a cuboid?
Make sure you
start with the
selection arrow
from the toolbox
From the Graph
menu select New
Parameter enter
5 and click cm
dot
1. Create a parameter of 5 cm. Remember to set as cm.
Construct –
circle by centre
and radius
Click on line
segment draw
line from centre
of circle to the
circu,mference
which will turn
pale blue when
you are correctly
positioned
(Hold down shift
to keep line
straight)
3. Create a circle of radius 5 cm.
Select the circle
with the arrow
and Display –
Hide Circle or
use Control and
H
Double click on
centre of circle to
mark Centre of
Rotation
Highlight line and
end point.
Transform
Rotate 90
degrees, mark
new centre and
repeat
Highlight point E
and line AB
Construct –
Parallel line.
Highlight line and
circle Construct
– Intersection or
Control I
2. Place a point on the page. Select point and the parameter
4. Draw a line segment horizontally equal in length to the radius of the circle
t1 = 5.00 cm
5. Hide the circle
6. Rotate the line segment repeatedly
through 90 degrees to form a square
t1 = 5.00 cm
D
C
7. Add line segment BE and using
the
Parameter as radius construct a
circle centre E
E
A
8. Construct a line parallel to AB
through E
B
9. Draw line segment from E to point of intersection F. Hide the circle and the
line.
10. Complete the rear square by rotating line segment FE as before.
t1 = 5.00 cm
H
G
11. Add line segments AF, DG and CH
To undo an
unwanted move
or set of moves
use Control Z
and to redo a
move use
Control R
Highlight the line
segment and
Construct –
midpoint or
Control M
With four points
selected
Construct Quadrilateral
Interior or
Control P.
With
quadrilateral
highlighted Edit
– Action Buttons
– Hide/Show.
Right click on
button to change
its colour and
label
D
C
F
E
12. Experiment by moving different
edges and vertices, especially vertex B
A
B
12. Mark the midpoints of each edge.
14. In turn highlight a set of 4 midpoints or vertices to form a quadrilateral
representing a plane of symmetry. Fill the interior of the quadrilateral and create
a hide/show button.
Hide Vertical 1
t1 = 5.00 cm
H
G
D
C
F
E
A
B
15. Create a set of planes of symmetries as above each with its own hide/show
button.
Show Vertical 1
Show Diagonal 1
Show Vertical 1
Hide vertical diagonal 1
Hide Diagonal 1
Show vertical diagonal 1
t1 = 5.00 cm
H
G
t1 = 5.00 cm
H
G
D
D
C
C
F
F
A
A
E
E
B
B