Warm-Up
Exercises
Bell Work
Find the coordinates of the image of A(–3, 8) for each
transformation.
1. Reflection in the x-axis.
2. Rotation of 90º about the origin
3.
Translation 4 units down
Warm-Up
Exercises
Notes
Definitions
A figure in the plane has line symmetry if the figure can
be mapped onto itself by a reflection in a line.
The line of reflection is a line of symmetry. A figure can
have more than one line of symmetry
Warm-Up
Exercises
Notes
http://commons.wikimedia.org/wiki/File:Peacock_Butterfly_(7822792836).jpg
Warm-Up1Exercises
EXAMPLE
Identify lines of symmetry
How many lines of symmetry does the hexagon have?
a.
b.
a.
Two lines of
symmetry.
b. Six lines of
symmetry.
c.
c. One line of
symmetry.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
How many lines of symmetry does the object appear
to have?
1.
2.
ANSWER
8
3.
ANSWER
5
ANSWER
1
Warm-Up
Exercises
Notes
Definitions
A figure in the plane has rotational symmetry if the
figure can be mapped onto itself by a rotation of 180° or
less about the center of the figure.
This point is the center of symmetry. A figure can have
more than one line of symmetry.
Note: the rotation can be either clockwise or counterclockwise.
Warm-Up2Exercises
EXAMPLE
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.
Warm-Up2Exercises
EXAMPLE
Identify rotational symmetry
b.
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.
Warm-Up2Exercises
EXAMPLE
Identify rotational symmetry
c.
Trapezoid
SOLUTION
c.
The trapezoid does not have
rotational symmetry because no
rotation of 180° or less maps the
trapezoid onto itself.
Warm-Up
Exercises
GUIDED
PRACTICE
Does the figure have rotational symmetry? If so,
describe any rotations that map the figure onto itself.
5.
Rhombus
6.
Octagon
SOLUTION
SOLUTION
yes; 180° about
yes; 90° or 180°
the center
about the center
7.
Right triangle
SOLUTION
no
Warm-Up
Exercises
Example
Warm-Up
Exercises
Example
Warm-Up
Exercises
Example
Warm-Up
Exercises
Example
Warm-Up
Exercises
Example
Warm-Up
Exercises
Example
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
How many lines of symmetry does each figure have?
1.
A Rhombus that is not a square
ANSWER
2
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
How many lines of symmetry does each figure have?
2.
Equilateral triangle
ANSWER
3
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Does the figure have rotational symmetry? If so,
describe the rotations that map the figure onto itself.
3.
ANSWER
Yes; 72° , 144°
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Does the figure have rotational symmetry? If so,
describe the rotations that map the figure onto itself.
4.
ANSWER
no
Warm-Up
Exercises
For Tomorrow
Homework
HW: 9.6 (pg. 614-615) #6-12,27-30