Understand the definitions of an angle, circle, perpendicular line, parallel line, and line segment. Transformations in geometry are represented in the plane using different methods, with transformations described as functions taking one point to another. Analyze transformations that preserve distance and angle with those that don't. Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon.

Use angles, circles, perpendicular lines, parallel lines, and line segments to define rotations, reflections, and translations. Given a geometric figure and a transformation, draw the transformed figure. Use rigid motion transformations to decide if two figures are congruent. Show that two triangles are congruent if corresponding sides and angles are congruent. Understand how triangle congruence criteria (ASA, SAS, and SSS) are supported by the definition of congruence in terms of rigid motions.

Prove theorems about lines and angles, including vertical angles being congruent and congruence of alternate interior angles and corresponding angles when a transversal crosses parallel lines. Prove theorems about triangles and parallelograms. Conduct formal geometric constructions using tools such as compass and straightedge. Construct an equilateral triangle, square, and