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STANDARDS

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US-NY

Math

New York Math

Geometry: Geometry - Similarity, Right Triangles, and Trigonometry

Understand similarity in terms of similarity transformations.

GEO-G.SRT.1

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

GEO-G.SRT.1.a

Fully covered
Verify experimentally that 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.
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GEO-G.SRT.1.b

Fully covered
Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

GEO-G.SRT.2

Partially covered
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

GEO-G.SRT.3

Fully covered
Use the properties of similarity transformations to establish the AA~, SSS~, and SAS~ criterion for two triangles to be similar.

Prove theorems involving similarity.

GEO-G.SRT.4

Fully covered
Prove and apply similarity theorems about triangles.

GEO-G.SRT.5

Use congruence and similarity criteria for triangles to:

GEO-G.SRT.5.a

Fully covered
Solve problems algebraically and geometrically.

GEO-G.SRT.5.b

Mostly covered
Prove relationships in geometric figures.

Define trigonometric ratios and solve problems involving right triangles.

GEO-G.SRT.6

Mostly covered
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent ratios for acute angles.

GEO-G.SRT.7

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

GEO-G.SRT.8

Partially covered
Use sine, cosine, tangent, the Pythagorean Theorem and properties of special right triangles to solve right triangles in applied problems.

Apply Trigonometry to general triangles.

GEO-G.SRT.9

Not covered
Justify and apply the formula A=(1/2)ab sin (C) to find the area of any triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
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