2.11 Mapping and Rotational Symmetry

Front

What is rotational symmetry?

Back

Rotational symmetry is a property of a shape that looks the same after a certain amount of rotation. The angle of rotation is the smallest angle that allows the shape to map onto itself.

Front

Define line of reflection.

Back

A line of reflection is a line across which a shape is flipped to create a mirror image. The original shape and its image are equidistant from the line.

Front

What is the smallest angle of rotation for a regular polygon with n sides?

Back

The smallest angle of rotation for a regular polygon with n sides is 360°/n.

Front

How do you determine if a line of reflection maps a polygon onto itself?

Back

To determine if a line of reflection maps a polygon onto itself, check if each point on the polygon is equidistant from the line and that the reflected points coincide with the original points.

Front

What is the significance of the angle of rotation in symmetry?

Back

The angle of rotation indicates how far a shape can be turned around a center point before it looks the same. It is crucial for understanding rotational symmetry.

Front

What is a trapezoid?

Back

A trapezoid is a four-sided figure (quadrilateral) with at least one pair of parallel sides.

Front

Explain the concept of mapping in geometry.

Back

Mapping in geometry refers to the transformation of a shape or figure from one position to another, which can include reflections, rotations, translations, and dilations.

Front

What does it mean for a polygon to map onto itself?

Back

For a polygon to map onto itself means that after a transformation (like rotation or reflection), the polygon appears unchanged.

Front

What is the role of the center of rotation?

Back

The center of rotation is the fixed point around which a shape is rotated. The distance from this point to any point on the shape remains constant during the rotation.

Front

How can you identify lines of symmetry in a shape?

Back

Lines of symmetry can be identified by folding the shape along a line and checking if both halves match perfectly.