6th Grade Math Textbook, Fundamentals

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Describe the symmetries of a regular octagon.

A regular octagon has line symmetry.

It has 8 lines of symmetry.

A regular octagon also has rotational

symmetry. It can be rotated 8 times.

Its angle of rotation is 45.

A regular octagon also has point symmetry.

It can be rotated 180.

1

Lesson 10-10 for exercise sets.

This figure matches for turns

of 90 , 180 , 270 , and 360.

1

Each of the following figures has rotational symmetry.

This figure matches for

turns of 120 , 240 , and 360.

3

This figure matches for

turns of 180 and 360.

2

Think

Figures with an angle of

rotation of 180 look the

same upside down as

right-side up!

The flower at the top of the preceding page has 5 possible rotations.

So the angle of rotation is , or 72. The angle measures of the other turns

are multiples of 72. They are 144 , 216 , 288 and 360.

Point symmetry is a special kind of rotational symmetry. A figure

has if it matches the original figure after rotating

the figure half a turnaround its center point. Figures with point

symmetry always have an angle of rotation of 180.

point symmetry

360

5

2 1

3 4 5 6 7 8

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Identify the types of symmetry that exist for each figure. Then describe them.

5.Discuss and Write Draw a figure that has both line symmetry and

rotational symmetry. Draw the line(s) of reflection and the center

of rotation, and list the angles of rotation.