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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.
Standard #: MAFS.912.G-CO.2.6Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand congruence in terms of rigid motions. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Educational Software / Tool
  • Transformations Using Technology # This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.
Formative Assessments
  • Congruent Trapezoids # Students will determine whether two given trapezoids are congruent.
  • Transform This # Students are asked to translate and rotate a triangle in the coordinate plane and explain why the pre-image and image are congruent.
  • Repeated Reflections and Rotations # Students are asked to describe what happens to a triangle after repeated reflections and rotations.
Lesson Plans
  • Coding Geometry Challenge #23 & 24 # This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.
  • Where Will I Land? # This is a beginning level lesson on predicting the effect of a series of reflections or a quick review of reflections for high school students.
  • How do your Air Jordans move? # In this inquiry lesson, students are moving their individually designed Air Jordans around the room to explore rigid transformations on their shoes. They will Predict-Observe-Explain the transformations and then have to explain their successes/failures to other students.
  • Congruence vs. Similarity # Students will learn the difference between congruence and similarity of classes of figures (such as circles, parallelograms) in terms of the number of variable lengths in the class. A third category will allow not only rigid motions and dilations, but also a single one-dimensional stretch, allowing more classes of figures to share sufficient common features to belong.
  • Transformers 3 # Students will learn the vocabulary of three rigid transformations, reflection, translation, and rotation, and how they relate to congruence. Students will practice transforming figures by applying each isometry and identifying which transformation was used on a figure. The teacher will assign students to take pictures of the three transformations found in the real world.
Problem-Solving Tasks
  • Reflections and Isosceles Triangles # This activity uses rigid transformations of the plane to explore symmetries of classes of triangles.
  • Reflections and Equilateral Triangles # This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles
  • Building a tile pattern by reflecting octagons # This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.
  • Building a tile pattern by reflecting hexagons # This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.
MFAS Formative Assessments
  • Congruent Trapezoids # Students will determine whether two given trapezoids are congruent.
  • Repeated Reflections and Rotations # Students are asked to describe what happens to a triangle after repeated reflections and rotations.
  • Transform This # Students are asked to translate and rotate a triangle in the coordinate plane and explain why the pre-image and image are congruent.
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