Use rigid motions for congruence

What you'll learn

1. State the formal definition of congruence in terms of rigid motions: two figures are congruent if and only if there exists a sequence of rigid motions (translations, reflections, rotations) that maps one figure exactly onto the other
2. Predict the effect of a given rigid motion on a given figure, including the positions of all vertices and the orientation of the image
3. Apply a sequence of rigid motions to transform a figure and verify that the image coincides with a target figure
4. Determine whether two given figures are congruent by finding a rigid motion (or sequence of rigid motions) that maps one onto the other, or by arguing that no such rigid motion exists
5. Explain why the rigid-motion definition of congruence is equivalent to the intuitive notion of "same shape and size"

Prerequisites

• Define transformations formally
• Draw transformed figures