Serving Up Symmetry
Man made and natural patterns
made to order!
What am I Learning Today?
Symmetry
How will I show that I learned it?
Determine and explain lines of symmetry and
rotational symmetry for different objects
Identify objects that have symmetrical
properties
Vocabulary
 Line symmetry: Figures that match exactly when
folded in half
 Rotational symmetry: Figures that line back up with
itself when rotated 180 degrees or less around its
center
 Transformation: Moving a figure without changing
its size or shape
 Translation: Movement of a figure along a straight
line
 Rotation: Movement of a figure around a point
 Reflection: When a figure flips over a line creating
a mirror image
Questions
What is line
symmetry?
Answers
When folded in half, the figure will completely cover itself.
Do all shapes have Some figures will have more than one line of symmetry,
line symmetry?
while others will have none.
What is a line
OF symmetry?
What is
rotational
symmetry?
The line that splits the shape
When a shape fits ONTO itself two or more
times in one full turn. The shape is rotated
about a fixed point.
This shape has 90 degree
rotational symmetry because it
fits onto itself 4 times, every 90o,
in one rotation.
Which of the following figures have
line symmetry?
Draw the figures that have symmetry on your paper and add
the lines of symmetry.
Is there symmetry in the Alphabet?
 Find at least three letters of the alphabet
that have only ONE vertical line of
symmetry.
 Find at least three letters of the alphabet
that have only ONE horizontal line of
symmetry.
 Find the four letters that have both types of
symmetry.
Symmetry in Nature
Symmetry in Art and Architecture
How do you determine the
degrees of rotational symmetry?
A full turn is a 360°
1
__
rotation. So a 4 turn
1
__
is 90°, and a
turn
2
is 180°.
360°
90°
180°
Where would 120° of rotational symmetry be?
What about 270°? Or 45°?
Draw a 180° rotation about the
point shown.
Trace the figure and the
point of rotation.
Place your pencil on the
point of rotation.
Rotate the figure 180°.
Trace the figure in its new
location.
Which is true about the figure
below?
A. The figure has rotational
symmetry after a 45° turn.
B. The figure has rotational
symmetry after 90 ° turn.
C. The figure has rotational
symmetry after a 120 ° turn.
D. The figure does not have rotational
symmetry.
When an object rotates it turns. So,
rotational symmetry means turn
symmetry.
How many times can you turn the object below and
it matches up with itself?
What degree of rotational symmetry does it have?
Questions
What are the three
types of
transformations?
What is a
rotation?
What is a
reflection?
What is a
translation?
Answers
Rotation, reflection, and translation
When a shape is rotated, or turned, around
a central point.
When a shape is flipped to create a mirror image.
When a shape slides over into a new place, but
position stays the same.
A rotation is the movement of a figure
around a point. A point of rotation can be
on or outside a figure.
The location and position of a figure
can change with a rotation.
When a figure flips over a line, creating a mirror
image, it is called a reflection. The line the figure
is flipped over is called line of reflection.
The location and position of a figure
change with a reflection.
A translation is the movement of a
figure along a straight line.
Only the location of the figure
changes with a translation.
Tell whether each is a translation,
rotation, or reflection.
The figure is flipped
over a line.
It is a reflection.
Tell whether each is a translation,
rotation, or reflection.
The figure moves
around a point.
It is a rotation.
Tell whether each is a translation,
rotation, or reflection.
The figure is moved
along a line.
It is a translation.
Objects with Rotational Symmetry