CCSS.Math.Content.HSG-CO.B.6
The standard
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 Mathematics
What this standard means
Students need to describe translations, rotations, and reflections using clear geometric language, then use those motions to move a figure or predict where it lands. They should track points, sides, angles, orientation, and distance without relying only on how a picture looks.
Mastery means students can give a sequence of rigid motions that maps one figure onto another, or explain why no such sequence works. Students often mix up rotation direction, lose track of corresponding vertices, or think figures are congruent just because they look similar or have matching angle measures.
Ways to teach it
- Hands-on activity: Give students cut-out triangles on grid paper and have them slide, flip, and turn one to match another, recording each move.
- Discussion or writing prompt: Ask, “What exact moves would carry figure A onto figure B, and how do you know distances stayed the same?”
- Quick assessment: Show two quadrilaterals on a coordinate grid and ask students to list corresponding vertices and one valid rigid motion sequence.
- Real-world connection: Use a floor tile pattern and have students identify translations, rotations, and reflections that move one tile onto another.
Plan a lesson for CCSS.Math.Content.HSG-CO.B.6
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSG-CO.B
Understand congruence in terms of rigid motions
- CCSS.Math.Content.HSG-CO.B.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and correspondin...
- CCSS.Math.Content.8.G.A.2
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and trans...
- CCSS.Math.Content.HSG-CO.B.8
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.