Geometry: Similarity, Right Triangles, and Trigonometry (G-SRT)

G-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor:G-SRT.10Prove the Laws of Sines and Cosines and use them to solve problems.G-SRT.11Understand 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.2Given 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.G-SRT.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.G-SRT.4Prove 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.G-SRT.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.G-SRT.6Understand 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.7Explain and use the relationship between the sine and cosine of complementary angles.G-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.G-SRT.9Derive 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.
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