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

Domain - Congruence

Cluster - Prove geometric theorems and, when appropriate, the converse of theorems.

[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.

Resources:


  • 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).

Predecessor Standards:

  • 8.G.A.5
    Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • 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.
  • GEO.G-CO.C.9
    Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, and conversely prove lines are parallel; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
  • GEO.G-CO.C.11
    Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
  • GEO.G-SRT.A.3
    Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
  • GEO.G-SRT.B.4
    Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
  • GEO.G-SRT.C.7
    Explain and use the relationship between the sine and cosine of complementary angles.