Standard - NY-8.G.2:
Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.

Standard - NY-8.G.3:
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Standard - NY-8.G.4:
Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.

Standard - NY-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.

Standard - NY-8.G.6:
Understand a proof of the Pythagorean Theorem and its converse.

Standard - NY-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.

Standard - NY-8.G.8:
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Standard - NY-8.G.9:
Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems.