Similarity, Right Triangles, & Trigonometry
- Understand Similarity In Terms Of Similarity Transformations
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G.SRT.1Verify experimentally the properties...more
Verify experimentally the properties of dilations given by a center and a scale factor:
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G.SRT.1.aA dilation takes a line not passing ...more
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
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G.SRT.1.bThe dilation of a line segment is lo...more
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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G.SRT.2Given two figures, use the definitio...more
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.
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G.SRT.3Use the properties of similarity tra...more
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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- Prove Theorems Involving Similarity
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G.SRT.4Prove theorems about triangles. Theo...more
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.
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G.SRT.5Use congruence and similarity criter...more
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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- Define Trigonometric Ratios And Solve Problems Involving Right Triangles
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G.SRT.6Understand that by similarity, side ...more
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.
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G.SRT.7Explain and use the relationship bet...more
Explain and use the relationship between the sine and cosine of complementary angles.
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G.SRT.8Use trigonometric ratios and the Pyt...more
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
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- Apply Trigonometry To General Triangles
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G.SRT.9(+) Derive the formula A = 1/2 ab si...more
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
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G.SRT.10(+) Prove the Laws of Sines and Cosi...more
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
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G.SRT.11(+) Understand and apply the Law of ...more
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
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Major cluster will be a majority of the assessment, Supporting clusters will be assessed through their success at supporting the Major Clusters and Additional Clusters will be assessed as well. The assessments will strongly focus where the standards strongly focus.
Grade level
- K-2
- 3-5
- 6-8
- 9-12
- math_attach
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