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Topic: Similarity, Right Triangles, and Trigonometry
Common Core Mathematics 912
Cluster
Understand similarity in terms of similarity transformations
Grade 912
G.SRT.1.
Verify experimentally the properties of dilations given by a center and a scale factor:
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.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.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.
G.SRT.3.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Cluster
Prove theorems involving similarity
Grade 912
G.SRT.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.
G.SRT.5.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Cluster
Define trigonometric ratios and solve problems involving right triangles
Grade 912
G.SRT.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.
G.SRT.7.
Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.8.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Cluster
Apply trigonometry to general triangles
Grade 912
G.SRT.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.
G.SRT.11.
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).