|ACADEMIC STANDARDS - MATH - GEOMETRY
STANDARDS FOR MATH
The geometric skills and concepts developed in this discipline are useful to all students. Aside from these skills and concepts, all students will develop their ability to construct formal logical arguments and proofs in geometric settings and problems.
- All students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
- All students write geometric proofs, including proofs by contradiction.
- All students construct and judge the validity of a logical argument. This includes giving counter examples to disprove a statement.
- All students prove basic theorems involving congruence and similarity.
- All students prove triangles are congruent or similar and are able to use the concept of corresponding parts of congruent triangles.
- All students know and are able to use the Triangle Inequality Theorem.
- All students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
- All students know, derive, and solve problems involving perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
- All students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres.
- All students compute areas of polygons including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
- All students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
- All students find and use measures of sides, interior and exterior angles of triangles and polygons to classify figures and solve problems.
- All students prove relationships between angles in polygons using properties of complementary, supplementary, vertical, and exterior angles.
- All students prove the Pythagorean Theorem.
- All students use the Pythagorean Theorem to determine distance and find missing lengths of sides of right triangles.
- All students perform basic constructions with straightedge and compass such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
- All students prove theorems using coordinate geometry, including the midpoint of a line segment, distance formula, and various forms of equations of lines and circles.
- All 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, (e.g., tan(x) = sin(x)/cos(x), (sin (x))2 + (cos (x))2 = 1).
- All 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.
- All students know and are able to use angle and side relationships in problems with special right triangles such as 30-60-90 triangles and 45-45-90 triangles.
- All students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
- All students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflection.