CCSS.Math.Content.HSG-CO.B.7
The standard
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 corresponding pairs of angles are congruent.
Common Core State Standards for Mathematics
What this standard means
Students need to connect triangle congruence to rigid motions. They should be able to argue that one triangle can be moved by translations, rotations, and reflections to land exactly on another when all matching sides and angles agree. They also need to explain the reverse, if a rigid motion matches one triangle to another, then matching sides and angles must be equal.
Mastery looks like a clear sequence of moves plus correct matching of vertices, sides, and angles. Students often get stuck naming corresponding parts, assuming triangles are congruent from the picture, or treating resizing as allowed. Keep the focus on distance and angle measures staying unchanged.
Ways to teach it
- Give pairs triangle cutouts and have students translate, rotate, or reflect one to fit the other, then label all corresponding parts.
- Ask students to write: How do rigid motions prove two triangles are the same size and shape without measuring everything again?
- Show two labeled triangles and ask students to list the corresponding sides, angles, and one possible rigid motion sequence.
- Use floor tile patterns or road signs to find congruent triangles and describe the moves that map one triangle onto another.
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Related standards
- CCSS.Math.Content.HSG-CO.B
Understand congruence in terms of rigid motions
- 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.