Geometry Standards
After standard title is standard number
G corresponds to Geometry
T corresponds to Trigonometry
The number corresponds to that topics California standard
Patterns, Lines, and Planes
· Patterns and Reasoning (G1)
· Transformations and Symmetry (G22)
· Conjectures (G3)
· Points, Lines, and Planes (G1)
· Segments and Their Measures (G1, 16)
· Angles (G1, 13, 16)
· Bisecting Segments and Angles (G16)
Triangles and Polygons
· Types of Angles (G1, 13)
· Classifying Triangles (G1, 13, 16)
· Types of Polygons (G12)
· Parallelograms (G12, 13 16)
· Building Prisms
Reasoning in Geometry
· Inductive and Deductive Reasoning (G1)
· Postulates, Definitions, and Properties (G1)
· Paragraph Proof (G1, 2, 3)
· Two-Column Proof (G1, 2, 3)
· Converses of Statements (G1, 2, 3)
· Pythagorean Theorem (G14, 15)
· Negations and Contrapositives (G1, 2, 3)
Coordinates in Geometry
· Finding Distances and Midpoints
· Equations of Lines (A6, 7)
· Exploring Parallels and Perpendiculars (G16, A8)
· Equations of Circles
· Coordinates and Proof (G17)
· Coordinates in Three Dimensions (G22)
Parallel Lines
· Parallel Lines and Transversals (G1, 7)
· Properties of Parallel Lines (G1, 7)
· Conditions for Parallel Lines (G1, 7)
· Proving Theorems About Parallels (G1, 7)
· Parallels in Space (G1, 7)
· Constructing Parallels and Perpendiculars (G16)
Conjectures About Triangles
· Triangle Inequalities (G6)
· Exploring Congruence (G1, 4, 5)
· Congruent Triangles: SSS, SAS, ASA, AAS, HL (G1, 2, 3, 4, 5)
· Applying Congruence (G1, 2, 3, 4, 5)
· Properties of Isosceles Triangles (G1, 12)
· Altitudes, Medians, and Bisectors (G1, 2, 3, 4, 5, 12, 13)
Quadrilaterals, Areas, and Volumes
· Classifying Quadrilaterals (G1, 7, 12)
· Identifying Parallelograms (G1, 12, 13)
· Conditions for Special Parallelograms (G1, 12, 13)
· Areas of Triangles and Quadrilaterals (G10, 12)
· Areas of Regular Polygons and Circles (G7, 10, 12)
· Prisms and Cylinders (G8, 9, 11)
Using Transformations
· Using Reflections
· Reflections with Coordinates
· Translations (all areas fall under G1, 22)
· Applying Rotations
· Glide Reflections
· Dilations
Similar Polygons
· Properties of Similar Figures (G1, 4)
· Similar Triangles (G1, 4, 5, 13)
· Proportions and Similarity (G1, 4, 5, 13)
· Areas and Volumes of Similar Figures (G1, 4, 5, 8, 9, 10, 11, 13)
· Geometric Probability (G1)
Applying Right Triangles
· Similar Right Triangles (G1, 4, 5, 13,)
· Special Right Triangles (G20)
· Sine, Cosine, and Tangent Ratios (G18, 19, 20)
· Using Vectors
· Areas and Trigonometry (G8, 10, 12, 18, 19, 20)
· Pyramids and Cones (G8, 9, 11)
Circles and Spheres
· Angles and Circles (G1, 7, 21)
· Tangents, Secants, and Chords (G21)
· Sectors and Arc Lengths (G8, 9, 21)
· Surface Areas and Volumes of Spheres (G8, 9)
· Volumes of Similar Solids (G8, 9, 11)
· Spherical Geometry
Coordinates for Transformations
· Dilations with Matrices
· Translations with Matrices
· Multiplying Matrices
· Reflections with Matrices
· Rotations with Matrices
Trigonometric Functions
· Angles (Trig. 1.0)
· Trigonometric Functions (Trig. 2.0, 3.0, 3.1, 3.2, 5.0, 6.0)
Acute Angles and Right Triangles
· Trigonometric Functions of Acute Angles (Trig. 19)
· Trigonometric Functions of Non-Acute Angles (Trig. 19)
· Solving Right Triangles (Trig. 12)
Radian Measure and the Circular Functions
· Radian Measure (Trig. 1.0)
· Circular Functions of Real Numbers (Trig. 2.0)
· Linear and Angular Velocity
Graphs of the Circular Functions
· Graphs of the Sine and Cosine Functions (Trig. 2.0, 4.0)
· Translating Graphs of the Sine and Cosine Functions (Trig. 4.0)
· Graphs of the Other Circular Functions (Trig. 5.0, 6.0, 8.0)
Applications of Trigonometry and Vectors
· Oblique Triangles and the Law of Sines (Trig. 13.0, 14.0)
· The Ambiguous Case of the Law of Sines (Trig. 13.0)
· The Law of Cosines (Trig. 13.0)