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Math

Mississippi Math

Integrated Mathematics II: Geometry: Similarity, Right Triangles, and Trigonometry (G-SRT)

Understand similarity in terms of similarity transformations

G-SRT.1

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

G-SRT.1.a

Fully covered
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.

G-SRT.1.b

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

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 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

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

Prove theorems involving similarity

G-SRT.4

Mostly covered
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

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

Define trigonometric ratios and solve problems involving right triangles

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 trigonometric ratios for acute angles.

G-SRT.7

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

G-SRT.8

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