Consider the object shown in each photograph as a plane...

Consider the object shown in each photograph as a plane figure.
a. State how many symmetry lines each figure has.
b. State whether or not the figure has a symmetry point.
c. List all the rotational symmetries of each figure between $0^{\circ}$ and $360^{\circ} .$
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Key Concepts

Point Symmetry

Point symmetry, also known as central symmetry, occurs when every part of a figure has a corresponding part equidistant from a central point in the opposite direction. This concept is significant because it describes a type of symmetry where the figure can be invariant under a 180° rotation, and it is crucial in identifying whether a shape has a unique center of symmetry.

Line Symmetry

This concept refers to the property of a plane figure where one or more lines (called axes of symmetry) can be drawn such that the figure is divided into two mirror-image halves. Understanding line symmetry is fundamental in assessing how a shape can be reflected over an axis and remain unchanged, which is essential in many areas of geometry and design.

Rotational Symmetry

Rotational symmetry involves a plane figure being capable of being rotated (by an angle less than 360°) about a central point such that it appears unchanged. This concept is key in geometry as it relates to how a shape can map onto itself after certain rotations, and it is critical when determining all the rotational invariances of a figure.

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