Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations

What you'll learn

1. Define congruence precisely: two figures are congruent if and only if one can be mapped onto the other by a sequence of rigid motions (translations, reflections, and rotations)
2. Explain why the transformation-based definition of congruence replaces and strengthens the informal "same shape and size" description
3. Identify and describe a specific sequence of rigid motions that maps one figure onto a given congruent figure, specifying the parameters of each transformation (direction/distance, line of reflection, center/angle of rotation)
4. Recognize that the order of transformations in a sequence matters -- different orderings can produce different results
5. Determine that two figures are NOT congruent when no sequence of rigid motions can map one onto the other, using measurement or visual reasoning to justify the conclusion

Prerequisites

• Lines are taken to lines, and line segments to line segments of the same length
• Angles are taken to angles of the same measure
• Parallel lines are taken to parallel lines