G.SRT

Similarity, Right Triangles, and Trigonometry

G.SRT.1(9/10) Use geometric constructions to verify the properties of dilations given by a center and a scale factor:G.SRT.10(+) 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.G.SRT.11(+) Prove the Laws of Sines and Cosines and use them to solve problems.G.SRT.12(+) 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).G.SRT.1a(9/10) 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.G.SRT.1b(9/10) The dilation of a line segment is longer or shorter in the ratio given by the scale factor.G.SRT.2(9/10) Recognize transformations as functions that take points in the plane as inputs and give other points as outputs and describe the effect of dilations on two-dimensional figures.G.SRT.3(9/10) Given two similar figures, describe a sequence of transformations that exhibits the similarity between them using coordinates and the non-coordinate plane.G.SRT.4(9/10) Understand the meaning of similarity for two-dimensional figures as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.G.SRT.5(9/10) Construct arguments about triangles using theorems. 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, and AA.G.SRT.6(9/10) Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.G.SRT.7(9/10) Show 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.G.SRT.8(9/10) Explain and use the relationship between the sine and cosine of complementary angles.G.SRT.9(9/10) Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
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