COS

** 1 ** || Determine the equation of a line given two points, a point and a slope, a table of values, a graph, ordered pairs, or the equation of a line parallel or perpendicular to a second line through a given point. || ** 2 ** || Prove theorems related to pairs of angles, including vertical, adjacent, complementary, and supplementary, as well as those formed by parallel lines cut by a transversal and perpendicular lines. || ** 3 ** || Justify relationships among different classes of polygons by using their properties. || ** 4 ** || Apply proportional reasoning to determine missing lengths of sides, measures of angles, and ratios of perimeters and areas of similar polygons. || ** 5 ** || Determine the measure of interior and exterior angles associated with polygons. || ** 5a ** || Verifying formulas for measures of interior and exterior angles of polygons inductively and deductively || ** 6 ** || Solve problems, including application-based problems, using properties and theorems related to circles, quadrilaterals, and other geometric shapes. || ** 6a ** || Determining the center and radius of a circle given its equation || ** 6b ** || Determining the equation of a circle given its center and radius || ** 7 ** || Apply the Pythagorean Theorem and its converse to solve application problems, including expressing answers in simplified radical form or as decimal approximations and using Pythagorean triples where applicable. || ** 7a ** || Proving the Pythagorean Theorem || ** 8 ** || Apply properties of special right triangles, including 30-60-90 and 45-45-90 triangles, to find missing side lengths. || ** 9 ** || Determine relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships. || ** 9a ** || Calculating the geometric mean to find missing lengths in right triangles. || ** 10 ** || Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. || ** 10a ** || Recognizing limitations of a conclusion through inductive reasoning || ** 10b ** || Using deductive reasoning to prove theorems || ** 10c ** || Using proof by negation to prove theorems || ** 10d ** || Writing conditional statements of a given conjecture || ** 11 ** || Solve for missing measures of sides and angles in right triangles by applying the right triangle ratios of sine, cosine, and tangent. || ** 12 ** || Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. || ** 13 ** || Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons. || ** 14 ** || Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated. || ** 15 ** || Classify polyhedra according to their properties, including the number of faces. || ** 15a ** || Identifying Euclidean solids (thank the state dept of education for inventing a new kind of geometric solid. I think they meant PLATONIC solids) || ** 16 ** || Calculate measures of arcs and sectors of a circle from given information. || ** 17 ** || Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids. || ** 17a ** || Deriving formulas for surface area and volume of spheres, cones and pyramids || ** 17b ** || Calculating specific missing dimensions of solid figures from surface area or volume || ** 17c ** || Determining the relationship between surface areas of similar figures and volumes of similar figures || ** 18 ** || Calculate probabilities arising in geometric contexts. ||