# Lesson 5Symmetries of Regular PolygonsSolidify Understanding

### 1.

What is the smallest fraction of a full circle that the wagon wheel needs to turn in order to appear the very same as it does now? How many degrees of rotation would that be?

### 2.

What is the smallest fraction of a full circle that the propeller needs to turn in order to appear the very same as it does right now? How many degrees of rotation would that be?

### 3.

What is the smallest fraction of a full circle that the Ferris wheel needs to turn in order to appear the very same as it does right now? How many degrees of rotation would that be?

## Set

### 4.

Draw the lines of symmetry for each regular polygon. Fill in the table, including an expression for the number of lines of symmetry in an -sided polygon.

Number

of Sides

Number

of Lines

of Symmetry

### 5.

Draw all of the diagonals in each regular polygon. Fill in the table and find a pattern. Is the pattern linear, exponential, or neither? How do you know? Attempt to find an expression for the number of diagonals in an -sided polygon.

Number

of Sides

Number

of Diagonals

### 6.

Find the angle(s) of rotation that will carry the -sided polygon below onto itself.

### 7.

What are the angles of rotation for a -gon? How many lines of symmetry (lines of reflection) will it have?

### 8.

What are the angles of rotation for a -gon? How many line of symmetry (lines of reflection) will it have?

### 9.

A regular polygon has rotational symmetry for an angle of . How many sides does it have? Explain.

### 10.

A regular polygon has rotation symmetry for an angle of . How many sides does it have? How many lines of symmetry does it have?

## Go

Use tools to make your work precise.

### 11.

Reflect point over the line of reflection and label the image .

### 12.

Reflect point over the line of reflection and label the image .

### 13.

Reflect triangle over the line of reflection and label the image .

### 14.

Reflect parallelogram over the line of reflection and label the image .

### 15.

Given triangle and its image , draw the line of reflection that was used.

### 16.

Given parallelogram and its image , draw the line of reflection that was used.