# Mathematics » Grade 8 » Geometry

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

• 8.G.1. Verify experimentally the properties of rotations, reflections, and translations:
• a. Lines are taken to lines, and line segments to line segments of the same length.
• b. Angles are taken to angles of the same measure.
• c. Parallel lines are taken to parallel lines.
• 8.G.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.
• 8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
• 8.G.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.
• 8.G.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.

## Understand and apply the Pythagorean Theorem.

• 8.G.6. Explain a proof of the Pythagorean Theorem and its converse.
• 8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
• 8.G.8. 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.

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