G-CO.A. Experiment with transformations in the plane

• Symmetries of a circle
• Tangent Lines and the Radius of a Circle
• Unit Squares and Triangles

G-CO.A.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

• Defining Parallel Lines
• Defining Perpendicular Lines

G-CO.A.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

• Dilations and Distances
• Fixed points of rigid motions
• Horizontal Stretch of the Plane

G-CO.A.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

• Origami regular octagon
• Seven Circles II
• Symmetries of a quadrilateral I
• Symmetries of a quadrilateral II
• Symmetries of rectangles

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

• Defining Reflections
• Defining Rotations
• Identifying Rotations
• Identifying Translations

G-CO.A.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

• Reflected Triangles
• Showing a triangle congruence: a particular case
• Showing a triangle congruence: the general case
• Trigonometric Identities and Rigid Motions