Slides, Flips and Turns
How does one create congruent shapes? In other words what can we do to a shape so that it keeps its shape and exact size? The answer is that we can do moves called slides, flips and turns. If we want to be fancy we can even combine a slide and a flip into a slide-flip.
All of the moves we will discuss fall into one of these four categories:
- An object is moved in one direction (the translation vector).
- An object is rotated around a point (the center of rotation).
- An object is reflected across a line (the reflection axis).
- A combination of a slide and a flip, flip across a line while sliding along that same line.
These moves are sometimes called a rigid motion. They are motions that do not distort shape. Picking something up and moving it around for instance is a rigid motion, but stretching or warping it is not. Because a rigid motion does not change size or shape, it is also called an isometry, from the Greek iso (meaning equal) and metry (meaning measure or distance).
If you have ever played Tetris, you will have used these rigid motions. Recall that the shapes used in Tetris consist of blocks made up of four squares.
To do well in the game we try to line up the game pieces so that there are no gaps. We are allowed to slide the game pieces left and right, and we are allowed to flip and turn the game pieces as well. In other words we are doing geometry when playing the game.