Geometry+Standards

// (Click on a Standard) //
 * __Geometry Standards__**


 * 1.0 ** Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.


 * 2.0 ** Students write geometric proofs, including proofs by contradiction.


 * 3.0 ** Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.


 * 4.0 ** Students prove basic theorems involving congruence and similarity.


 * 5.0 ** Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.


 * 6.0 ** Students know and are able to use the triangle inequality theorem.


 * 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.


 * 8.0 ** Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.


 * 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.


 * 10.0 ** Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.


 * 11.0 ** Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.


 * 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.


 * 13.0 ** Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.


 * 14.0 ** Students prove the Pythagorean theorem.


 * 15.0 ** Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.


 * 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.


 * 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.


 * 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.


 * 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.


 * 20.0 ** Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.


 * 21.0 ** Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.


 * 22.0 ** Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.