California Standards for Geometry Omega Math's Alignment to California Standards
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. Geometry - g1.1, Chapter 2
2.0 Students write geometric proofs, including proofs by contradiction. Geometry - g2.3
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. Geometry - g2.1, g2.2, g2.3
4.0 Students prove basic theorems involving congruence and similarity. Geometry - g2.2
5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. Geometry - g2.2
6.0 Students know and are able to use the triangle inequality theorem. Geometry - g3.1
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. Geometry - g1.3, g5.2, chapter 6
8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. Geometry - Chapter 7, Chapter 8, Chapter 9, Chapter 10
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. Geometry - Chapter 9, chapter 10
10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. Geometry - Chapter 8
11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. Geometry - Chapter 7, chapter 8
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. Geometry - g5.3
13.0 Students prove relationships between angles in polygon by using properties of complementary, supplementary, vertical, and exterior angles. Geometry - g1.2, g1.3, g3.1, g2.2, g2.3, g5.1, g5.3
14.0 Students prove the Pythagorean theorem. N/A
15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. Geometry - g4.1
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. Geometry - g1.1
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. Geometry - g2.3
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. Geometry - g4.3
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. Geometry - g4.3
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. Geometry - g4.2
21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. Geometry - Chapter 6
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. Geometry - g1.5