CCSS.Math.Content.HSG-CO.B
The standard
Understand congruence in terms of rigid motions
Common Core State Standards for Mathematics · High School — Geometry
What this standard means
Students need to see congruence as more than matching side lengths and angles. They should be able to use translations, rotations, and reflections to move one figure onto another, then explain why the figures are congruent because distance and angle measures stay the same.
Mastery looks like a student describing a sequence of rigid motions clearly and checking that corresponding parts match. Students often get stuck naming the correct transformation, especially rotation direction and center. They may also think figures are congruent only when they face the same way or sit in the same place.
Ways to teach it
- Use patty paper to trace a triangle, then slide, turn, and flip it onto a second triangle to test congruence.
- Ask students to write directions that move Figure A onto Figure B using only translations, rotations, and reflections.
- Show two figures on a grid and ask students to name one rigid motion sequence or explain why none works.
- Connect to floor tile patterns by having students identify slides, turns, and flips that create repeated congruent shapes.
Plan a lesson for CCSS.Math.Content.HSG-CO.B
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Related standards
- 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.6
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...
- 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.