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# California Academic Content Standards

### Use the links below to find resources that support standards adopted by the California State Board of Education

for English-language arts, mathematics, history-social science, science, and visual and performing arts.

The resource symbol indicates that there are resources matched to the grade, strand, concept, or standard.

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California Academic Content Standards1641507 9317

Strand Geometry65 285

- The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.
- Substrand 1.0Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.1 37
- Substrand 2.0Students write geometric proofs, including proofs by contradiction.1 9
- Substrand 3.0Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.1 11
- Substrand 4.0Students prove basic theorems involving congruence and similarity.1 15
- Substrand 5.0Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.1 20
- Substrand 6.0Students know and are able to use the triangle inequality theorem.1 7
- Substrand 7.0Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.1 32
- Substrand 8.0Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.1 77
- Substrand 9.0Students 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.1 31
- Substrand 10.0Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.1 32
- Substrand 11.0Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.1 28
- Substrand 12.0Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.1 37
- Substrand 13.0Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.1 13
- Substrand 14.0Students prove the Pythagorean theorem.1 25
- Substrand 15.0Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.1 27
- Substrand 16.0Students 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.1 35
- Substrand 17.0Students 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.1 19
- Substrand 18.0Students 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}= 1.1 9 - Substrand 19.0Students 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.1 9
- Substrand 20.0Students 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.1 1
- Substrand 21.0Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.1 18
- Substrand 22.0Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.1 71