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Transformational Geometry

The word "transform" means to change. In this unit, students explore changing the location of shapes by translations, reflections, and rotations. They identify which of these transformations represent an isometry (congruence transformation) and determine whether side length, angle measure, perimeter, area, and orientation are preserved in each of the three transformations. In addition, students investigate the relationship between the coordinates of a pre-image and the coordinates of its image.

Geometry: Transformational Geometry Activities

Title Type

Reflections and Rotations

Students will reflect figures over the x- and y-axes. By studying what happens to the coordinates of the pre-image and image points, they will write rules for reflecting points over the axes. Students will then rotate figures about the origin, in both clockwise and counterclockwise directions. Again, they will study what happens to the coordinates of the pre-image and image points to write rules for reflecting points 90° and 180° about the origin.

Alignments  Standards  |  Textbook  
  • 2618

Exploring Transformations

Investigate translating and reflecting shapes in the coordinate plane and observe how the new image is related to the original shape.

Alignments  Standards  |  Textbook  
  • 7249

Transformations: Translations

Investigate what a triangle will look like when it is translated horizontally or vertically.

Alignments  Standards  |  Textbook  
  • 6861

Transformations: Reflections

Explore what a reflection does to an object.

Alignments  Standards  |  Textbook  
  • 6803

Glide Reflections

Explore using a translated figure to create a glide reflection.

Alignments  Standards  |  Textbook  
  • 6455

Transformations With Lists

Students use list operations to perform reflections, rotations, translations and dilations on a figure, and graph the resulting image using a scatter plot.

Alignments  Standards  |  Textbook  
  • 4300

Tessellations with Regular Polygons

Explore regular polygons to find out which regular polygons will tessellate the plane.

Alignments  Standards  |  Textbook  
  • 6416

Transformations: Rotations

Explore clockwise and counterclockwise rotations to discover the properties of the pre-image and image of a triangle.

Alignments  Standards  |  Textbook  
  • 6919
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