Lesson 6 Symmetries of Regular Polygons Solidify Understanding

Ready

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 $n$ -sided polygon.

Number of Sides	Number of Lines of Symmetry
$3$
$4$
$5$
$6$
$7$
$8$
$n$

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 $n$ -sided polygon.

Number of Sides	Number of Diagonals
$3$
$4$
$5$
$6$
$7$
$8$
$n$

6.

Find the angle(s) of rotation that will carry the $12$ -sided polygon below onto itself.

7.

What are the angles of rotation for a $20$ -gon? How many lines of symmetry (lines of reflection) will it have?

8.

What are the angles of rotation for a $15$ -gon? How many line of symmetry (lines of reflection) will it have?

9.

A regular polygon has rotational symmetry for an angle of $18 °$ . How many sides does it have? Explain.

10.

A regular polygon has rotation symmetry for an angle of $20 °$ . 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 $A$ over the line of reflection and label the image $A^{'}$ .

12.

Reflect point $A$ over the line of reflection and label the image $A^{'}$ .

13.

Reflect triangle $A B C$ over the line of reflection and label the image $A^{'} B^{'} C^{'}$ .

14.

Reflect parallelogram $A B C D$ over the line of reflection and label the image $A^{'} B^{'} C^{'} D^{'}$ .

15.

Given triangle $X Y Z$ and its image $X^{'} Y^{'} Z^{'}$ , draw the line of reflection that was used.

16.

Given parallelogram $Q R S T$ and its image $Q^{'} R^{'} S^{'} T^{'}$ , draw the line of reflection that was used.