G.1.0: Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
G.4.0: Students prove basic theorems involving congruence and similarity.
G.5.0: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
G.6.0: Students know and are able to use the triangle inequality theorem.
G.7.0: Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
G.8.0: Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
G.9.0: Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
G.10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
G.11.0: Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
G.12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.
G.13.0: Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
G.14.0: Students prove the Pythagorean theorem.
G.15.0: Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
G.16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
G.17.0: Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
G.18.0: Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))² + (cos(x))² = 1.
G.19.0: Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
G.21.0: Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
G.22.0: Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
Correlation last revised: 9/11/2014