# California Standards for Geometry

California Standards for Geometry | Omega Math's Alignment to California Standards |
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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 |