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# Geometry: Similarity, Right Triangles, and Trigonometry619 preguntas32 habilidades

## HSG-SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor:

## 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.

## HSG-SRT.A.1b

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.
Pronto habrá nuevas habilidades para este estándar.

## 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.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

## 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.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

## 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.
Pronto habrá nuevas habilidades para este estándar.