During this unit, students will begin to develop detailed definitions. The work they will do will help them to explain the geometry in the world around them, communicating to solve problems. Geometric Transformations can be found in many careers, and I often take the time to point them out as often as possible.

  • Week 1 – Definitions (G.CO.A.1 & 2)
  • Week 2 – Rotations, Reflections, and Translations (G.CO.A.3, 4, & 5)
  • Week 3 – Congruence (G.CO.B.6)

Common Core State Standards for Mathematical Content

Congruence — G-CO
A. Experiment with transformations in the plane
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on
The undefined notions of point, line, the distance along a line, and distance around a circular arc.
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).
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections
that carry it onto itself.
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
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.
B. Understand congruence in terms of rigid motions
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.

Common Core State Standards for Mathematical Practice
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.


Unit 1 - Geometric Transformations