Geometry / Unit 4: Transformations
4.7 Rigid Motions and Congruence
Notes
Two figures are congruent if a sequence of rigid motions maps one onto the other.
- Rigid motions: translations, reflections, rotations. They keep lengths and angles.
- Two figures are similar if a sequence of rigid motions and dilations maps one onto the other.
- Example: a triangle reflected and then translated is congruent to the original.
Practice
A triangle is rotated $90^\circ$ and then dilated by a scale factor of 3. The image is:
The dilation changes the size, so the figures are similar but not congruent.
Which transformation does NOT always produce a congruent image?
A dilation with $k \ne 1$ changes lengths.
$\triangle ABC$ has $AB = 7$. After a reflection and a translation, what is $A'B'$?
Rigid motions keep lengths the same.
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