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Rotations, Reflections, and Translations of Geometric Shapes

HSG-CO.A.4
Answer Keys Here

Aligned To Common Core Standard:

High School Congruence - HSG-CO.A.4

What Are Rotations, Reflections, and Translations of Geometric Shapes? Transformation is an important concept in geometry and comprises of three sub-categories including translations, rotations, and reflections. To understand what these are, you can stand in front of the mirror and observe yourself when you move sideways and turn towards your side. What you observe in the mirror is exactly what rotations, translations, and reflections are in geometry. Reflection - The most straightforward concept here is that of reflection. It is a common term that we come across very frequently in our everyday lives. So, what is a reflection in geometry? It is flipping of a point or an entire shape over a mirror line. The mirror line serves as a mirror on the graph. Shape and its reflected image are congruent, and both these are equidistant from the mirror line. Rotation - Rotation is another term that we use almost every day in our lives. When tightening or loosening a screw you are rotating the screw at an axis of rotation. Similarly, in geometry, rotation is when we turn a shape around a fixed point, which serves as the axis of rotation. To rotate a shape on the graph, you will need the angle of rotation and the point of rotation. Translation - Translation is simple. A shape and its translated image will have the same orientation and only the vertices will move sideways or upwards or downwards relative to the vertices of a shape. Both the original shape and its translated form are congruent. Each vertex covers an equal distance. This selection of worksheets and lessons teach students to identify and process these three common geometric transformations.

Printable Worksheets And Lessons




Homework Sheets

These problems always remind me of origami. It looks like a set of instructions.

  • Homework 1 - Draw the line segment between the vertex and the point of rotation.
  • Homework 2 - Which diagram shows abcde's reflection?
  • Homework 3 - Which diagram shows ABCD rotated 20° counter clockwise about A?



Practice Worksheets

These problems require a higher level of thinking on the part of the kids.

  • Practice 1 - Use a protractor to draw the angle of rotation.
  • Practice 2 - A reflection flips the figure over a line to create a mirror image.
  • Practice 3 - Which diagram shows a mirror reflection down?



Math Skill Quizzes

I did get a little carried away with the mirrored reflections. I will add a better spread of problems in a few weeks.

  • Quiz 1 - Label each as a reflection, glide, or transformation.
  • Quiz 2 - Is this a reflection?
  • Quiz 3 - Use a compass to mark the rotated vertex point on the other side of the angle.