trigonometry
CCR.Math.Content.HSG-SRT.A.1
Verify experimentally the properties of dilations given by a center and a scale factor:
CCR.Math.Content.HSG-SRT.A.1a
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.
CCR.Math.Content.HSG-SRT.A.1b
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
CCR.Math.Content.HSG-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.
CCR.Math.Content.HSG-SRT.A.3
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
CCR.Math.Content.HSG-SRT.B.4
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.
CCR.Math.Content.HSG-SRT.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
CCR.Math.Content.HSG-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.
CCR.Math.Content.HSG-SRT.C.7
Explain and use the relationship between the sine and cosine of complementary angles.
CCR.Math.Content.HSG-SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.^{★}
CCR.Math.Content.HSG-SRT.D.9
(+) 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.
CCR.Math.Content.HSG-SRT.D.10
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
CCR.Math.Content.HSG-SRT.D.11
(+) 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).