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STANDARDS

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US-NC

Math

North Carolina Math

Grade 8: Geometry

Understand congruence and similarity using physical models, transparencies, or geometry software.

NC.8.G.2

Use transformations to define congruence.

NC.8.G.2.a

Partially covered
Verify experimentally the properties of rotations, reflections, and translations that create congruent figures.

NC.8.G.2.b

Fully covered
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.

NC.8.G.2.c

Mostly covered
Given two congruent figures, describe a sequence that exhibits the congruence between them.

NC.8.G.3

Fully covered
Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across x-axis and y-axis on two-dimensional figures using coordinates.

NC.8.G.4

Use transformations to define similarity.

NC.8.G.4.a

Not covered
Verify experimentally the properties of dilations that create similar figures.
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NC.8.G.4.b

Fully covered
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

NC.8.G.4.c

Fully covered
Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Analyze angle relationships.

NC.8.G.5

Use informal arguments to analyze angle relationships.

NC.8.G.5.a

Fully covered
Recognize relationships between interior and exterior angles of a triangle.

NC.8.G.5.b

Fully covered
Recognize the relationships between the angles created when parallel lines are cut by a transversal.

NC.8.G.5.c

Fully covered
Recognize the angle-angle criterion for similarity of triangles.

NC.8.G.5.d

Not covered
Solve real-world and mathematical problems involving angles.
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Understand and apply the Pythagorean Theorem.

NC.8.G.6

Fully covered
Explain the Pythagorean Theorem and its converse.

NC.8.G.7

Fully covered
Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.

NC.8.G.8

Fully covered
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

NC.8.G.9

Fully covered
Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.