Integrated Math 1 / Unit 8: Transformations and Congruence
8.1 Transformations and Rigid Motions
Notes
A transformation moves a figure in the plane. The original is the preimage; the result is the image (marked with a prime: $A'$).
- A rigid motion (isometry) keeps all side lengths and angle measures. Translations, reflections and rotations are rigid motions.
- A dilation changes size, so it is not a rigid motion.
- Rigid motions produce an image that is congruent to the preimage.
- Example: triangle $ABC$ maps to triangle $A'B'C'$, so $ABC$ is the preimage.
Practice
Which transformation is NOT a rigid motion?
A dilation changes side lengths, so the image is a different size.
What do all rigid motions preserve?
Distances and angles stay the same, so the image is congruent to the preimage.
Triangle $ABC$ is transformed into triangle $A'B'C'$. What is triangle $ABC$ called?
The original figure is the preimage and the new figure is the image.
Ready for more? Take the Unit 8 test.