Rigid Motions and Symmetry

Combine transformations and recognize symmetry.

Lesson 4 of 53 parts Practice Flashcards

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Rigid Motions

Objective: Distinguish rigid from non-rigid transformations.

Translations, reflections, and rotations preserve lengths and angle measures. Dilations with scale factor other than 1 are not rigid motions.

Left, a translated triangle keeps its size. Right, a dilated triangle grows, so dilation is not a rigid motion.

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Rigid Motions

Objective: Distinguish rigid from non-rigid transformations.

Translations, reflections, and rotations preserve lengths and angle measures. Dilations with scale factor other than 1 are not rigid motions.

Composing Transformations

Objective: Apply transformations in the stated order.

A composition applies one map after another; order can affect the result. For example, reflecting then translating need not match translating then reflecting.

A triangle is first reflected over the y-axis, then translated down 5 units.

Line and Rotational Symmetry

Objective: Identify a line of reflection symmetry and rotational symmetry.

A figure has line symmetry if reflection across a line maps it onto itself. It has rotational symmetry if a rotation of less than 360° maps it onto itself.

A regular hexagon has six lines of symmetry and maps onto itself after every 60-degree rotation.

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