Symmetry
Reflectional
Rotational
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
REFLECTION
REFLECTIONAL SYMMETRY
An easy way to understand reflectional symmetry is to
think about folding.
Do you
remember
What
happens
when
folding
a piece
of
you
unfold
the piece
paper,
ofdrawing
paper? half
of a heart, and then
cutting it out?
REFLECTIONAL SYMMETRY
Line of Symmetry
Reflectional
Symmetry
means that a shape
Thebe
two
halves
are a
can
folded
along
exactly
the same…so
line of reflection
The
two
halves
make
The
line
of
reflection
They
are of the
the two
halves
a in
whole
heart.
a
figure
with
symmetrical.
figure
match exactly,
reflectional
point
by point.
symmetry is called a
line of symmetry.
REFLECTIONAL SYMMETRY
The line created by the fold is the line of symmetry.
A shape can have more than one line of symmetry.
How
can is
I fold
Where
the line of symmetry for this shape?
this shape so
that it matches
exactly?
Line of Symmetry
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
REFLECTIONAL SYMMETRY
How many lines of symmetry does each regular shape have?
Do you see a pattern?
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
What about a circle?
Infinite lines of symmetry
What is true for every line
of symmetry?
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
REFLECTIONAL SYMMETRY
Which of these flags have reflectional symmetry?
United States of America
Canada
Mexico
England
ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after
you rotate less than one full turn, it is the
same as the original shape.
Here is an example… As this shape is rotated 360, is it
ever the same before the shape
returns to its original direction?
Yes, when it is rotated 90 it is the
same as it was in the beginning.
What other angles make it look like
the original?
90
180
270
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after
you rotate less than one full turn, it is the
same as the original shape.
Here is another example…
As this shape is rotated 360, is it
ever the same before the shape
returns to its original direction?
Yes, when it is rotated 180 it is the
same as it was in the beginning.
180
So this shape is said to have
rotational symmetry.
ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after
you rotate less than one full turn, it is the
same as the original shape.
Here is another example…
As this shape is rotated 360, is it
ever the same before the shape
returns to its original direction?
No, when it is rotated 360 it is
never the same.
So this shape does NOT have
rotational symmetry.
ROTATION SYMMETRY
Does this shape have rotational symmetry?
Yes, when the shape is
rotated 120 it is the
same. Since 120  is less
than 360, this shape
HAS rotational
symmetry.
Notice we can also rotate 240 
and have the same figure.
120
240 
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
ROTATION SYMMETRY
Does this shape have rotational symmetry?
Yes, when the
shape is rotated
any number of
degrees, it is the
same. This shape
HAS rotational
symmetry.
WHAT KINDS OF SYMMETRY?
Reflectional: 3 lines of symmetry
Rotational: 120° and 240°
WHAT KINDS OF SYMMETRY?
Propeller #2
Propeller #1
Reflectional (5 lines of symmetry) Rotational (72°) only
Rotational (360/5 = 72°)
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
WHAT KINDS OF SYMMETRY?
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
WHAT KINDS OF SYMMETRY?
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
WHAT KINDS OF SYMMETRY?
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.
Homework
pp. 621-624 (2-9, 13-15, 27-33)
G. CO. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.