Moving Geometric Figures

Congruent Figures:

Definition: Figures are congruent if they match exactly when one figure is placed on top of the other.

Examples:

Line segments are congruent if they have the same length.

Angles are congruent if they have the same degree measure.

Circles are congruent if they have the same diameter.

Polygons are congruent if all the angles of one polygon match exactly, and all the sides match exactly.

Reflections:

Definition:

A reflection of a figure is the ‘flipping’ of the figure over a line of reflection. The figure and the reflection have the same size and shape. The figure and its reflection are reversed. Each point on the figure and its matching point on the reflection are the same distance from the line of reflection.

Examples:

preimage (original figure)

reflection (reflected figure)

Translations:

Definition:

A translation moves a figure by “sliding” it to a new location.

Rotation:

A rotation moves a figure by “turning” it around a point.

Frieze Patterns:

Definition:

A frieze pattern is a design made up of shapes that are lined up.

Line of Symmetry:

Definition:

A line of symmetry is a dashed line drawn through a figure that divides the figure into 2 parts; both parts look exactly alike but are facing in opposite directions. To check, fold the figure over the line of symmetry. If the two halves match exactly, the figure is symmetric.

Some figures may have more than 1 line of symmetry.

A square has 4 lines of symmetry.