Standards Map

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 - Define trigonometric ratios and solve problems involving right triangles.

[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.

Resources:


  • Ratio
    A relationship between quantities such that for every a units of one quantity there are b units of the other. A ratio is often denoted by a:b and read “a to b”.

Predecessor Standards:

  • 7.RP.A.2
    Recognize and represent proportional relationships between quantities.
  • 7.RP.A.2.a
    Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  • 7.RP.A.2.b
    Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • 7.RP.A.2.c
    Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
  • 7.RP.A.2.d
    Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.G-SRT.A.3
    Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
  • MII.G-SRT.C.7
    Explain and use the relationship between the sine and cosine of complementary angles.
  • MII.G-SRT.C.8
    Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
  • MIII.F-TF.A.2
    Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
  • MIII.F-TF.C.8
    Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant.
  • MIII.G-SRT.D.10
    (+) Prove the Laws of Sines and Cosines and use them to solve problems.
  • PC.F-TF.C.9
    (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
  • PC.G-SRT.D.9
    (+) Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • PC.G-SRT.D.10
    (+) Prove the Laws of Sines and Cosines and use them to solve problems.
  • AQR.F-TF.C.9
    (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.