1. Learning Objective
We will determine1 if the given figure has line of Symmetry and Angle of rotation.
What are we going to do?
What is determine means?_____.
CFU
Activate Prior Knowledge
A rotation is a transformation around point P, the center of rotation. Every 90° of rotation moves the preimage around the origin by one quadrant,
Rotation
On your whiteboard, find the following points under the given rotation.
Activate Prior Knowledge CFU
Students, you already know how to find the points of rotation. Today, we will learn how to find the line of symmetry.
Make Connection
1 Figure out
Vocabulary

3. Skill Development/Guided Practice
A figure has line symmetry if it can be reflected across a line so that the image maps onto the preimage. The line of symmetry divides the figure into two congruent halves.
Pair-Share:
A: How many lines of symmetry does a circle have? Explain.
B: Does a circle have rotational symmetry? If so, what is the angle?
CFU
A circle has an infinite number of lines of symmetry because a line of symmetry is possible at every point of a circle.
A figure has rotational symmetry if it can be rotated around a point by an angle greater than 0° and less than 360° so that the image maps onto the preimage.
A circle has rotational symmetry because no matter what point is up, it will match itself. The angle of symmetry would be less than 1°.

4. Skill Development/Guided Practice
On your whiteboard, complete the explanation for Definition, Examples, and Vocabulary of Line Symmetry.

5. Skill Development/Guided Practice
On your whiteboard, complete the explanation for Definition, Examples, and Vocabulary of Rotational Symmetry.

6. Skill Development/Guided Practice
On your whiteboard:
360/3
360/2

7. Skill Development/Guided Practice
A figure has line symmetry if it can be folded in half over a line, and both halves are exactly the same. These lines are called lines of symmetry. A figure can have several different lines of symmetry. This figure has 2 lines of symmetry.
Steps to Finding the line of symmetry: 1 2 3
Trace the figure on a piece of tracing paper.
See if the figure can be folded along a straight line
Sketch the lines of symmetry on the figure.
1. On your whiteboard:
What do you have to know about any segments in a figure to decide whether the figure has line symmetry?
Pair-Share
Pairs of segments in the figure must have the same length, so that one half of the figure will coincide with the other half when the figure is folded across a line of symmetry.

8. name the angles of rotation
Skill Development/Guided Practice
A figure has rotational symmetry if it can be turned between 0° and 180°, and the figure looks exactly the same. The angle is called an angle of rotational symmetry. This figure has an angle of rotational symmetry of 90°.
Steps to Finding the line of symmetry: 1 2 3
Count the number of edges
Divide 360 by the number of edges
The other angles of rotation for the figure are just the multiples of step 2.
1. On your whiteboard: Describe the symmetry: Draw the lines of symmetry and
name the angles of rotation

9. Incorrect; the two diagonals are not lines of symmetry.
Skill Development/Guided Practice
Relevance Reason #1: Constructing an work of art:
Symmetry is widely used in designing cool work of art. It begins with one simple geometric figure, such as a triangle, square, or rectangle, on a piece of construction paper. Then other lines or two dimensional shapes to the figure are added. Next, identical copies of the figure are made and arranged in a symmetrical pattern.
Relevance Reason #2: Knowing how to find line of symmetry and angles of symmetry will help you do well on tests: (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..).
A student was asked to draw all of the lines of symmetry on each figure shown. Identify the student’s work as correct or incorrect. If incorrect, explain why.
Incorrect; the two diagonals are not lines of symmetry.
Incorrect; the figure has no lines of symmetry
Incorrect; the figure has three more lines of symmetry, each connecting the remaining pairs of opposite vertices.

10. What did you learn today about how to determine if the given figure has a line of Symmetry and Angle of Rotation.
Word Bank
Image & Preimage
Rotation
Center of rotation
Angle of Rotation.
Symmetry Line
SUMMARY CLOSURE
Today, I learned how to __________________
______________________________________________________________.