A circle of radius \(r\) with center \(O\) is the set of all points that are a distance \(r\) units from \(O\).

To draw a circle of radius 3 units and center \(O\), use a compass to draw all the points at a distance 3 units from \(O\).

Two figures are congruent if there is a rigid motion or a sequence of rigid motions (translations, rotations, and reflections) that takes one figure onto the other.

In this figure, Triangle A is congruent to Triangle D.

• A translation takes Triangle A onto Triangle B.
• A rotation takes Triangle B onto Triangle C.
• A reflection takes Triangle C onto Triangle D.

A directed line segment is a line segment that has distance (length) and direction.

The arrow on this directed line segment shows that it starts at point \(A\) and ends at point \(B\).

A line segment is the set of all points on a line between two endpoints.

Two lines that never intersect are called parallel. Line segments can also be parallel if they extend into parallel lines.

This figure shows two parallel line segments.

The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to the segment.

In this diagram, the dashed line is the perpendicular bisector of segment \(AB\).

A reflection is a rigid transformation that is defined by a line. It takes one point to another point that is the same distance from the given line, but on the other side. The segment from the original point to its image is perpendicular to the line of reflection.

In this figure, \(A\) is reflected across line \(m\), and \(A′\) is the image of \(A\) under the reflection.

A figure has reflection symmetry if there is a reflection that takes the figure onto itself.

In this diagram, the letter X has reflection symmetry over each of the dashed lines.

A regular polygon is a polygon where all of the sides are congruent and all of the angles are congruent.

A figure has rotation symmetry if there is a rotation that takes the figure onto itself. (This does not include rotations using angles, such as \(0^\circ\) and \(360^\circ\), that take every point on a figure back to its original position.)

This hexagon has rotation symmetry 60 degrees clockwise or counterclockwise around its center.​​​​​

A translation is a rigid transformation that is defined by a directed line segment. It takes one point to another point so that:

• The directed line segment from the original point to its image is parallel to the given directed line segment.
• Both directed line segments have the same length and direction.

In the figure shown here, \(A'\) is the image of \(A\) under the translation given by the directed line segment \(t\).