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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.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 definition of congruence in terms of rigid motions to decide if they are congruent.
 
  • 3D Transmographer
    This lesson contains an applet that allows students to explore translations, reflections, and rotations.
  • 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
  • Geometry in Tessellations
    In this lesson students will learn about lines, angles, planes, and experiment with the area and perimeter of polygons.
  • Quadrilaterals-Beyond Definition - A Practice Understanding Task
    Making and justifying properties of quadrilaterals using symmetry transformations (G.CO.3, G.CO.4, G.CO.6) Congruence, Construction and Proof Module - Task 7
  • Quadrilaterals-Beyond Definition - Teacher Notes
    Teacher notes for "Quadrilaterals-Beyond Definition - A Practice Understanding" task. (G.CO.3, G.CO.4, G.CO.6) Congruence, Construction and Proof Module - Task 7
  • Symmetries of Quadrilaterals - A Develop Understanding Task
    Finding rotational symmetry and lines of symmetry in special types of quadrilaterals (G.CO.3, G.CO.6) Congruence, Construction and Proof Module - Task 5
  • Symmetries of Quadrilaterals - Teacher Notes
    Teacher notes for the "Symmetries of Quadrilaterals - A Develop Understanding" task (G.CO.3, G.CO.6) Congruence, Construction and Proof Module - Task 5
  • Symmetries of Regular Polygons - A Solidify Understanding Task
    Examining characteristics of regular polygons that emerge from rotational symmetry and lines of symmetry (G.CO.3, G.CO.6) Congruence, Construction and Proof Module - Task 6
  • Symmetries of Regular Polygons - Teacher Notes
    Teacher notes for "Symmetries of Regular Polygons - A Solidify Understanding" task. (G.CO.3, G.CO.6) Congruence, Construction and Proof Module - Task 6
  • Tessellations: Geometry and Symmetry
    Students can explore polygons, symmetry, and the geometric properties of tessellations in this lesson.
  • Transformations and Frieze Patterns
    In two lessons, this unit will introduce students to the world of symmetry and rotation in figures and patterns. Students learn to recognize and classify symmetry in decorative figures and frieze patterns, and will also get the chance to create and classify their own figures and patterns using JavaSketchpad applets.
  • Translations, Reflections, and Rotations
    Students are introduced to the concepts of translation, reflection and rotation in this lesson plan.
  • Visual Patterns in Tessellations
    In this lesson students will learn about types of polygons and tessellation patterns around us.
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