Mathematics » Grade 8 » Geometry

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

• 1. Verify experimentally the properties of rotations, reflections, and translations:

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  • a. Lines are taken to lines, and line segments to line segments of the same length.

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  • b. Angles are taken to angles of the same measure.

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  • c. Parallel lines are taken to parallel lines.

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• 2. 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; given two congruent figures, describe a sequence that exhibits the congruence between them.

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• 3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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• 4. 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; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

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• 5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

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Understand and apply the Pythagorean Theorem.

• 6. Explain a proof of the Pythagorean Theorem and its converse.

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• 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

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• 8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

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

• 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

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