Standards Map

Mathematics > Course Model Geometry (Traditional Pathway) > Congruence
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Mathematics | Course : Model Geometry (Traditional Pathway)

Domain - Congruence

Cluster - Understand congruence in terms of rigid motions.

[GEO.G-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.

Resources:


  • ASA conguence
    Angle-side-angle congruence. When two triangles have corresponding angles and sides that are congruent, the triangles themselves are congruent.
  • Congruent
    Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations).
  • Rigid motion
    A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions are here assumed to preserve distances and angle measures.
  • SAS congruence (Side-angle-side congruence)
    When two triangles have corresponding sides and the angles formed by those sides are congruent, the triangles are congruent.
  • SSS congruence (side-side-side congruence)
    When two triangles have corresponding sides that are congruent, the triangles are congruent.

Predecessor Standards:

  • 7.G.A.2
    Draw (freehand, with ruler and protractor, and with technology) two-dimensional geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • GEO.G-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 definition of congruence in terms of rigid motions to decide if they are congruent.
  • GEO.G-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 corresponding pairs of angles are congruent.
  • GEO.G-CO.C.10
    Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent, and conversely prove a triangle is isosceles; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
  • GEO.G-SRT.B.5
    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.