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Mathematics - Secondary Curriculum
Secondary Mathematics I [2011]
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Understand congruence in terms of rigid motions.
Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems.
G.CO.8
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
 
  • Congruence
    The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics 1 Cluster "Experiment with transformations in the plane" / Standards G.CO.1, G.CO.2, G.CO.3, G.CO.4 and G.CO.5 and Cluster "Understand congruence in terms of rigid motions" / Standards G.CO.6, G.CO.7 and G.CO.8 and Cluster "Make geometric constructions" / Standards G.CO.12 and G.CO.13.
  • Congruent Triangles - A Solidify Understanding Task
    Establishing the ASA, SAS and SSS criteria for congruent triangles. (G.CO.6, G.CO.7, G.CO.8) Congruence, Construction and Proof Module - Task 9
  • Congruent Triangles - Teacher Notes
    Teacher notes for "Congruent Triangles - A Solidify Understanding" task. (G.CO.6, G.CO.7, G.CO.8) Congruence, Construction and Proof Module - Task 9
  • Congruent Triangles to the Rescue - A Practice Understanding Task
    Working with systems of linear equations, including inconsistent and dependent systems (G.CO.7, G.CO.8) Congruence, Construction and Proof Module - Task 10
  • Congruent Triangles to the Rescue - Teacher Notes
    Teacher notes for "Congruent Triangles to the Rescue - A Practice Understanding" task. (G.CO.7, G.CO.8) Congruence, Construction and Proof Module - Task 10
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