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Mathematics > Course Model Mathematics II (Integrated Pathway) > Similarity, Right Triangles, and Trigonometry
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Similarity, Right Triangles, and Trigonometry

Cluster - Understand similarity in terms of similarity transformations.

[MII.G-SRT.A.3] - Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.

Resources:


  • AA similarity
    Angle-angle similarity. When two triangles have corresponding angles that are congruent, the triangles are similar.
  • Similarity transformation
    A rigid motion followed by a dilation.

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:

  • MII.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.
  • MII.G-SRT.A.2
    Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • MII.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.
  • MII.G-SRT.B.5
    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
  • MII.G-SRT.C.6
    Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.