CA GE 1.0
|
Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
|
CA GE 2.0
|
Students write geometric proofs, including proofs by contradiction. If a line L is tangent to a circle at a point P, prove that the radius passing through P is perpendicular to L.
|
CA GE 3.0
|
Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
|
CA GE 4.0
|
Students prove basic theorems involving congruence and similarity.
|
CA GE 5.0
|
Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
|
CA GE 6.0
|
Students know and are able to use the triangle inequality theorem.
|
CA GE 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.
|
CA GE 8.0
|
Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
|
CA GE 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.
|
CA GE 10.0
|
Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
|
CA GE 11.0
|
Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
|
CA GE 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.
|
CA GE 13.0
|
Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
|
CA GE 14.0
|
Students prove the Pythagorean theorem.
|
CA GE 15.0
|
Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
|
CA GE 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.
|
CA GE 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.
|
CA GE 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))? + (cos(x))? = 1.
|
CA GE 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.
|
CA GE 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.
|
CA GE 21.0
|
Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
|
CA GE 22.0
|
Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
|