Geometry

8.G.1Verify experimentally the properties of rotations, reflections and translations: (MP.5, MP.6)8.G.2Understand 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. (MP.2, MP.7)8.G.3Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. (MP.3, MP.5, MP.6)8.G.4Understand 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. (MP.2, MP.5, MP.7)8.G.5Use 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. (MP.3)8.G.6Explain a proof of the Pythagorean Theorem and its converse. (MP.3, MP.7)8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (MP.1, MP.2, MP.4)8.G.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (MP.5, MP.6)8.G.9Apply the formulas for the volumes and surface areas of cones, cylinders and spheres and use them to solve real-world and mathematical problems. (MP.1, MP.7, MP.8)
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