Standard - GEO.G.CO.1:
Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.

Standard - GEO.G.CO.2:
Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.

Standard - GEO.G.CO.3:
Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.

Standard - GEO.G.CO.4:
Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.

Standard - GEO.G.CO.5:
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.

Standard - GEO.G.CO.6:
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Standard - GEO.G.CO.7:
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Standard - GEO.G.CO.8:
Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.

Standard - GEO.G.CO.9:
Prove and apply theorems about lines and angles.

Standard - GEO.G.CO.10:
Prove and apply theorems about triangles.

Standard - GEO.G.CO.11:
Prove and apply theorems about parallelograms.

Standard - GEO.G.CO.12:
Make, justify, and apply formal geometric constructions.

Standard - GEO.G.CO.13:
Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.