Introduction

Translations, reflections, and rotations are rigid transformations that move objects in a coordinate plane and hold congruence. In this unit, you have learned how to transform a figure using a given translation, reflection, or rotation rule. In this lesson you will transform figures by using a combination of two or more rigid transformations. This process is called composition of transformations

To introduce the compositions of transformations, use the Composition of Transformations activity from GeoGebra to complete the 8.06 Exploring Compositions task.

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Use graph paper and/or software to draw and identify a sequence of transformations that will carry a given figure onto another
  • Show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other

Essential Questions

  • How can you change a figure’s position with changing its size and shape?
  • How can we identify the transformation of a figure in a coordinate plane?
  • After performing a sequence of transformations on a figure, will the resulting image have the same size and shape?

Enduring Understandings

  • Shape and area can be conserved during mathematical transformations.
  • The symmetry of polygons can be described in rotations and reflections.
  • We can use x and y coordinates to calculate translations in the coordinate plane.
  • Rotations, reflections and translations are examples that preserve angles and distances.
  • Geometric transformations are functional relationships.

The above objectives correspond with the Alabama Course of Study: Geometry standard: 21, 21a, 22, 22a, 22b, 24.