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STANDARDS

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US-SC

Math

South Carolina Math

Geometry: Similarity, Right Triangles, and Trigonometry

G.GSRT.1

Fully covered
Understand 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. Verify experimentally the properties of dilations given by a center and a scale factor. Understand the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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G.GSRT.2

Mostly covered
Use the definition of similarity to decide if figures are similar and justify decision. Demonstrate that two figures are similar by identifying a combination of translations, rotations, reflections, and dilations in various representations that move one figure onto the other.

G.GSRT.3

Mostly covered
Prove that two triangles are similar using the Angle-Angle criterion and apply the proportionality of corresponding sides to solve problems and justify results.

G.GSRT.4

Prove, and apply in mathematical and real-world contexts, theorems involving similarity about triangles, including the following:

G.GSRT.4a

Mostly covered
A line drawn parallel to one side of a triangle divides the other two sides into parts of equal proportion.

G.GSRT.4b

Mostly covered
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

G.GSRT.4c

Fully covered
The square of the hypotenuse of a right triangle is equal to the sum of squares of the other two sides.

G.GSRT.5

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

G.GSRT.6

Partially covered
Understand how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.

G.GSRT.7

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

G.GSRT.8

Fully covered
Solve right triangles in applied problems using trigonometric ratios and the Pythagorean Theorem.