- A
*symmetry*of an object is a motion of that object that doesn't change its size or shape. That is, a symmetry is something you do to an object.

Examples for objects in the plane: slide the object (officially called*translation*); turn it around (officially called*rotation*); flip it over, or replace it with its mirror image (officially called*reflection*); flip it, then slide (officially called*glide reflection*).

In fact, these 4 motions are the only types of symmetries for objects in the plane. For more details, including pictures, see The 4 plane symmetries. - An object or pattern
*has symmetry*of a certain type if it looks the same when that symmetry is done to it.

Examples: A valentine heart has reflection symmetry: reflection across its center line switches its right and left halves, so afterwards it still looks the same. A pinwheel has rotational symmetry: if you rotate it by 90 degrees, it looks the same.

- Make a pattern using only copies of the house that has rotational
symmetry
**and**reflection symmetry. - Make a pattern using only copies of the house that has translation symmetry and no other symmetries.
- Make a pattern using only copies of the house that has glide reflection symmetry and no other symmetries.
- Make a pattern using only copies of the house that has translation symmetry and rotation symmetry.
- What other combinations of symmetries can you make with copies of the house?
- Can you find a symmetric pattern of houses that tessellates the plane (covers the whole plane with no gaps or overlaps)?

To: Math Forum: ICME 8 || California Math Show at Cal State San Bernardino