Louisiana: Similarity, Right Triangles, and Trigonometry Math Standards
9 standards · 3 domains
UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS.
- GM:G-SRT.A.1.a 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.
- GM:G-SRT.A.1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- GM: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.
- GM:G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
PROVE AND APPLY THEOREMS INVOLVING SIMILARITY.
- GM:G-SRT.B.4 Prove and apply 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; SAS similarity criteria; SSS similarity criteria; ASA similarity.
- GM:G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
DEFINE TRIGONOMETRIC RATIOS AND SOLVE PROBLEMS INVOLVING RIGHT TRIANGLES.
- GM:G-SRT.C.6 Understand that by similarity, side ratios in right triangles, including special right triangles (30-60-90 and 45-45-90), are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- GM:G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
- GM:G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.