Geo/Trig Standards

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)