8-11 Symmetry

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

8-11 Symmetry

Warm UpTrue or false?

1. In a vertical reflection, the original figure is flipped over a line of symmetry.

2. In a translation, the original figure slides along a straight line and is flipped.

3. In a rotation, a figure is moved around a point.

false

false

true

8-11 Symmetry

Problem of the Day

Name four plane figures that can be rotated 180° around a center point and look the same after the rotation as they did before.

Possible answer: rectangle, square, parallelogram, regular hexagon

8-11 Symmetry

Learn to identify symmetry.

8-11 Symmetry

Vocabulary

line symmetryline of symmetryrotational symmetry

8-11 Symmetry

A figure has line symmetry if it can be folded or reflected so that the two parts of the figure match, or are congruent. The line of reflection is called the line of symmetry.

8-11 Symmetry

Additional Example 1A: Identifying Lines of Symmetry

Determine whether each dashed line appears to be a line of symmetry.

The two parts of the figure appear to match exactly when folded or reflected across the line.

The line appears to be a line of symmetry.

8-11 Symmetry

Additional Example 1B: Identifying Lines of Symmetry

Determine whether each dashed line appears to be a line of symmetry.

The two parts of the figure do not appear congruent.

The line does not appear to be a line of symmetry.

8-11 Symmetry

Check It Out: Example 1A

Determine whether each dashed line appears to be a line of symmetry.

The two parts of the figure do not appear congruent.

The line does not appear to be a line of symmetry.

8-11 Symmetry

Check It Out: Example 1B

Determine whether each dashed line appears to be a line of symmetry.

The two parts of the figure appear to match exactly when folded or reflected across the line.

The line appears to be a line of symmetry.

8-11 Symmetry

Some figures have more than one line of symmetry.

8-11 Symmetry

Additional Example 2A: Finding Multiple Lines of Symmetry

Find all of the lines of symmetry in the regular polygon.

Trace the figure and cut it out.

Fold the figure in half in different ways.

Count the lines of symmetry.

5 lines of symmetry

8-11 Symmetry

Additional Example 2B: Finding Multiple Lines of Symmetry

Find all of the lines of symmetry in the regular polygon.

Count the lines of symmetry.

8 lines of symmetry

8-11 Symmetry

Additional Example 2C: Finding Multiple Lines of Symmetry

Find all of the lines of symmetry in the regular polygon.

Count the lines of symmetry.

4 lines of symmetry

8-11 Symmetry

Check It Out: Example 2A

Find all of the lines of symmetry in the regular polygon.

1 line of symmetry

Count the lines of symmetry.

8-11 Symmetry

Check It Out: Example 2B

Find all of the lines of symmetry in the regular polygon.

Count the lines of symmetry.

4 lines of symmetry

8-11 Symmetry

Check It Out: Example 2C

Find all of the lines of symmetry in the regular polygon.

Count the lines of symmetry.

4 lines of symmetry

8-11 Symmetry

Additional Example 3A: Social Studies Application

Find all of the lines of symmetry in the flag.

Alaska

There are no lines of symmetry.

8-11 Symmetry

Additional Example 3B: Social Studies Application

Find all of the lines of symmetry in the flag.

Arizona

1 line of symmetry

8-11 Symmetry

Additional Example 3C: Social Studies Application

Find all of the lines of symmetry in the flag.

Colorado

1 line of symmetry

8-11 Symmetry

2 lines of symmetry

Additional Example 3D: Social Studies Application

Find all of the lines of symmetry in the flag.

New Mexico

8-11 Symmetry

Check It Out: Example 3A

2 lines of symmetry

Find all of the lines of symmetry in each design.

8-11 Symmetry

There are no lines of symmetry.

Check It Out: Example 3B

Find all of the lines of symmetry in each design.

8-11 Symmetry

1 line of symmetry

Check It Out: Example 3C

Find all of the lines of symmetry in each design.

8-11 Symmetry

2 lines of symmetry

Check It Out: Example 3D

Find all of the lines of symmetry in each design.

8-11 Symmetry

A figure has rotational symmetry if it can be rotated about a point by an angle less than 360° so that it coincides with itself.

8-11 Symmetry

Additional Example 4A: Identifying Rotational Symmetry

Tell whether each figure has rotational symmetry.

Each time the figure is rotated 90° about its center, the image looks like the original figure.

The figure has rotational symmetry.

8-11 Symmetry

Additional Example 4B: Identifying Rotational Symmetry

Tell whether each figure has rotational symmetry.

For any rotation less than 360°, the image never looks like the original figure.

The figure does not have rotational symmetry.

8-11 Symmetry

Check It Out: Example 4A

Tell whether each figure has rotational symmetry.

For any rotation less than 360°, the image never looks like the original figure.

The figure does not have rotational symmetry.

8-11 Symmetry

Check It Out: Example 4B

Tell whether each figure has rotational symmetry.

Each time the figure is rotated 180° about its center, the image looks like the original figure.

The figure has rotational symmetry.

8-11 Symmetry

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

8-11 Symmetry

Lesson Quiz

Does the described figure have line symmetry?

1. right isosceles triangle

2. rectangle

Do the following capital letters of the alphabet

have symmetry? If so, is the line of symmetry

horizontal or vertical? Do the letters have

rotational symmetry?

3. H 4. R

yes

yes

yes, vertical and horizontal; yes

no; no

8-11 Symmetry

1. Identify the figure which does not have line symmetry.

A. B.

C. D.

Lesson Quiz for Student Response Systems

8-11 Symmetry

2. Identify the figure which has line symmetry.

A. B.

C. D.

Lesson Quiz for Student Response Systems

8-11 Symmetry

3. Does the capital letter E of the alphabet have line symmetry? If so, is the line of symmetry horizontal, vertical, or both?

A. yes, horizontal B. yes, vertical

C. yes, both D. no

Lesson Quiz for Student Response Systems

8-11 Symmetry

4. Does the capital letter J of the alphabet have line symmetry? If so, is the line of symmetry horizontal, vertical, or both?

A. yes, horizontal B. yes, vertical

C. yes, both D. no

Lesson Quiz for Student Response Systems