Problem Set A
1) Determine the number of lines of symmetry in each figure below.
| How many lines of Symmetry? | ||
| Equilateral Triangle |  | |
| Square |  | |
| Regular Pentagon |  | |
| Regular Hexagon |  |
Now use your results above to come up with a general rule for the number of lines of symmetry for regular polygons.
| For a regular polygon with n sides, ________________________________________________________________. |
2) Draw a figure that matches each description:
a. has no symmetry.
b. has vertical symmetry, but not horizontal symmetry, and a rotational symmetry of any degree.
3) Determine all the symmetries in each shape.
a.  | b.  | c.  |
d.  | e.  |
4) Consider the capital letters of the alphabet. Group them all into 4 categories: horizontal symmetry, vertical symmetry, point symmetry (180° rotation), or no symmetry. Letters may be used in more than one group.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
| Vertical Line Symmetry | Horizontal Line Symmetry |
| Point Symmetry | No Symmetry |
5) Design a corporate logo that has horizontal symmetry but not vertical symmetry, and a rotational symmetry less than 180°.
6) ABCDEFGH is a polygon with reflectional symmetry over line 
. If the perimeter of the polygon is 46 and 
is 7, what is the perimeter of polygon ABCDH? Write an explanation to justify your solution.
7) HART is vertically symmetric, ∠HTR = (6x + 13)°, and ∠ATR = (4x – 12)°.
Find the measure of ∠HTA.
∠ is the symbol for angle. It refers to the ‘space between’ segments or lines. In the diagram, we could label the information ∠ATR = 4x − 12 like: 
8) Draw in the necessary squares to give the figure symmetry required.
a. Horizontal Symmetry | b. Vertical Symmetry |
| c. Point Symmetry | d. 90° rotational symmetry about the origin |
9) Color in the necessary squares so that the figure will have reflectional symmetry over the line shown.
a.  | b.  |
c.  | d.  |
10) Is there any shape that has an infinite number of lines of symmetry? If so, draw it and explain how it has an infinite number. If not, explain why it is impossible.
11) Mazzy and Star are arguing about the number of lines of symmetry a rectangle has. Mazzy says 2 but Star says 4. Who do you agree with and why do you think the other persons guess is wrong?
12) a. Suppose you are tracking the person who stole cookies from the cookie jar. The person left a clear set of tracks to follow. The distance between steps from toe to heel is approximately 5 inches. If each foot print is 9 inches long, about how far did the person travel if you counted a total of 39 steps?
12b. This picture above is an example of what two transformations?
