1. Congruence

2. Definition of Congruence:
Two figures are congruent if they are identical in size and shape. They do not need to have the same orientation.

3. Transformations: translation
A translation is a transformation in which every point on the figure has moved a fixed distance in a given direction.

4. Transformations: reflection
A reflection is a transformation in which the shape is reflected about a mirror line.

5. Transformations: rotation
A rotation is a transformation in which every point on the figure is turned through a given angle about a fixed point.

9. Activity: Polyominoes
Dominoes are shapes formed from two adjacent squares.
How many different dominoes are there?
By different, we mean:
How many dominoes are there which are not congruent?

10. Activity: Polyominoes
Let’s do the same problem, this time with three squares:
The square must be completely adjacent:
i.e. is good, but is not.
How many different triominoes are there?

11. Activity: Polyominoes
Now consider 4 squares and then 5 squares. How many different tetrominoes (made from 4 squares) are there? How many different pentominoes (made from 5 squares) are there? Is there a pattern? If you found all of the pentominoes, can you form a rectangle using each one only once?