Honors Geometry
Lesson 9.6
Identify Symmetry
Line Symmetry
•  A figure in the plane has line symmetry
if the figure can be mapped onto itself
by a reflection line.
Line of Symmetry
•  The line of reflection.
EXAMPLE 1
Identify lines of symmetry
How many lines of symmetry does the hexagon have?
a.
b.
SOLUTION
a.
Two lines of
symmetry.
c.
SOLUTION
SOLUTION
b. Six lines of
symmetry.
c. one line of
symmetry.
for Example 1
GUIDED PRACTICE
How many lines of symmetry does the object appear
to have?
1.
2.
3.
ANSWER
ANSWER
8
Could argue 4
5
ANSWER
1
GUIDED PRACTICE
4.
for Example 1
Draw a hexagon with no lines of symmetry.
ANSWER
Rotational Symmetry
•  A figure in the plane has rotational
symmetry if the figure can be mapped
onto itself by a rotation of 180º or less
about the center of the figure.
Center of Symmetry
•  The point of rotational symmetry.
EXAMPLE 2
Identify rotational symmetry
Does the figure have rotational symmetry? If so,
describe any rotations that map the figure onto itself.
a.
Parallelogram
SOLUTION
a.
The parallelogram has rotational
symmetry. The center is the
intersection of the diagonals. A 180°
rotation about the center maps the
parallelogram onto itself.
EXAMPLE 2
b.
Identify rotational symmetry
Regular octagon
SOLUTION
b. The regular octagon has rotational
symmetry. The center is the
intersection of the diagonals.
Rotations of 45o, 90o, 135o, or 180°
about the center all map the
octagon onto itself.
EXAMPLE 2
c.
Identify rotational symmetry
Trapezoid
SOLUTION
c.
The trapezoid does not have
rotational symmetry because no
rotation of 180° or less maps the
trapezoid onto itself.
EXAMPLE 3
Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
SOLUTION
The triangle has line symmetry. Three
lines of symmetry can be drawn for the
figure.
For a figure with s lines of symmetry,
the smallest rotation that maps the
figure onto itself has the measure .
360o .So, the equilateral triangle has
s
360o or 120o rotational symmetry.
3
The correct answer is B.