GEOMETRY

Standard 1. 

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

Standard 2. 

Students write geometric proofs, including proofs by contradiction

Standard 3. 

Students construct and judge the validity of a logical argument, and this includes giving counter examples to disprove a statement

Standard 4. 

Students prove basic theorems involving congruence and similarity

Standard 5. 

Students prove triangles are congruent or similar and are able to use the concept of corresponding parts of congruent triangles

Standard 6. 

Students know and are able to use the Triangle Inequality Theorem

Standard 7. 

Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles

Standard 8. 

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

Standard 9. 

Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres

Standard 10. 

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

Standard 11.

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

Standard 12. 

Students find and use measures of sides, interior and exterior angles of triangles and polygons to classify figures and solve problems

Standard 13. 

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

Standard 14. 

Students prove the Pythagorean Theorem

Standard 15. 

Students use the Pythagorean Theorem to determine distance and find missing lengths of sides of right triangles

Standard 16. 

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

Standard 17. 

Students prove theorems using coordinate geometry, including the midpoint of a line segment, distance formula, and various forms of equations of lines and circles

Standard 18. 

Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle, and they also know and are able to use elementary relationships between them, tan(x) = sin(x)/cos(x)

Standard 19. 

Students use trigonometric functions to solve for an unknown side of a right triangle, given an angle and a side

Standard 20. 

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

Standard 21. 

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

Standard 22. 

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