Pentominoes Symmetry

A pentomino is like a domino, but has 5 squares instead of 2. The squares must be arranged to share a side. Examples of triominoes (made with 3 squares) are shown in the shaded areas here:

Notice that any rotation of the triomino is still the same shape. For example, the following triominoes are all considered the same shape, because simply rotating the first triomino can form the two on the right.

These are all the same. Do not count a rotation as a new shape!

a) Using graph paper, color all the pentominoes (5 squares which share at least one side) possible. Be careful not to count rotated pentominoes as different shapes.

b) List all pentominoes containing at least one line of symmetry.

c) Indicate the total line(s) of symmetry for each of the symmetric pentominoes. You may draw the lines or give the number of lines of symmetry.

d) Discuss which pentominoes can be reflected to create a new shape. In other words, which pentominoes can be flipped over to create a new shape, without making the same shape created by rotating the original shape?