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# High School: Geometry: Similarity, Right Triangles, and Trigonometry

#### HSG.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.

#### HSG.SRT.A.1.b

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

### 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.

### HSG.SRT.A.3

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

### 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.

### 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.

### HSG.SRT.C.7

Explain and use the relationship between the sine and cosine of complementary angles.

### 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.
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### HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

### 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.