Geometry and Measurement

8.GM.1Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).8.GM.1aVerify that lines are mapped to lines, including parallel lines.8.GM.1bVerify that corresponding angles are congruent.8.GM.1cVerify that corresponding line segments are congruent.8.GM.2Apply the properties of rigid transformations (rotations, reflections, translations).8.GM.2aRotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.8.GM.2bReflect geometric figures with respect to the x-axis and/or y-axis.8.GM.2cTranslate geometric figures vertically and/or horizontally.8.GM.2dRecognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.8.GM.2eGiven two congruent figures, describe the series of rigid transformations that justifies this congruence.8.GM.3Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).8.GM.3aUse coordinate geometry to describe the effect of transformations on two-dimensional figures.8.GM.3bRelate scale drawings to dilations of geometric figures.8.GM.4Apply the properties of transformations (rotations, reflections, translations, dilations).8.GM.4aDilate geometric figures using scale factors that are positive rational numbers.8.GM.4bRecognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.8.GM.4cGiven two similar figures, describe the series of transformations that justifies this similarity.8.GM.4dUse proportional reasoning to find the missing side lengths of two similar figures.8.GM.5Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.8.GM.5aDiscover that the sum of the three angles in a triangle is 180 degrees.8.GM.5bDiscover and use the relationship between interior and exterior angles of a triangle.8.GM.5cIdentify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.8.GM.5dRecognize that two similar figures have congruent corresponding angles.8.GM.6Use models to demonstrate a proof of the Pythagorean Theorem and its converse.8.GM.7Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.8.GM.8Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.8.GM.9Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.
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