Example: Translate by $\langle 3, -2 \rangle$: $(1, 4) \to (4, 2)$

Reflections (Flips)

Every point is mirrored across a line of reflection.

Rotations (Turns)

Rotating about the origin counterclockwise:

Congruence Through Transformations

Two figures are congruent if one can be mapped to the other using a sequence of rigid transformations.

$\triangle ABC \cong \triangle DEF$

means there exists a combination of translations, reflections, and/or rotations that maps $\triangle ABC$ exactly onto $\triangle DEF$.

Key principle: Rigid transformations preserve distances, angle measures, and parallelism.