Q: If a design maintains all characteristics when it is rotated about a point it has symmetry?

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No. Objects can have reflective symmetry but no rotational symmetry.

Axial symmetry.

all characteristics true

Not exactly. Rotational symmetry means that a shape will look the same if the object is rotated around some axis, by ANY angle.There are no specific requirements as to where the axis must be.

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False

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Reflectional symmetry

No. Objects can have reflective symmetry but no rotational symmetry.

Axial symmetry.

Axial symmetry.

Axial symmetry.

False

all characteristics true

Reflectional symmetry