1. Fundamentals of Geometry

• 1.1 Points, Lines, Planes, and Angles
  • 1.1.1 Understanding Points, Lines, and Planes
  • 1.1.2 Measuring and Constructing Segments
  • 1.1.3 Measuring and Constructing Angles
  • 1.1.4 Pairs of Angles

• 1.2 Coordinate and Transformation Tools
  • 1.2.1 Using Formulas in Geometry
  • 1.2.2 Midpoint and Distance in the Coordinate Plane
  • 1.2.3 Transformations in the Coordinate Plane

2. Reasoning and Writing Geometric Proofs

• 2.1 Inductive and Deductive Reasoning
  • 2.1.1 Using Inductive Reasoning to Make Conjectures
  • 2.1.2 Conditional Statements
  • 2.1.3 Using Deductive Reasoning to Verify Conjectures
  • 2.1.4 Biconditional Statements and Definitions

• 2.2 Mathematical Proof
  • 2.2.1 Algebraic Proof
  • 2.2.2 Geometric Proof
  • 2.2.3 Flowchart and Paragraph Proofs

3. Parallel and Perpendicular Lines

• 3.1 Lines with Transversals
  • 3.1.1 Planes, Lines, and Angles
  • 3.1.2 Angles, Parallel Lines, and Transversals
  • 3.1.3 Proving that Lines are Parallel
  • 3.1.4 Properties of Perpendicular Lines

• 3.2 Slope and the Equation of a Line
  • 3.2.1 Finding the Slope Given Two Points
  • 3.2.2 Slope-Intercept Form
  • 3.2.3 Point-Slope Form
  • 3.2.4 Slopes of Parallel and Perpendicular Lines

4. Triangle Congruence

• 4.1 Triangles and Congruence
  • 4.1.1 Classifying Triangles
  • 4.1.2 Angle Relationships in Triangles
  • 4.1.3 Congruent Triangles

• 4.2 Proving Triangle Congruence
  • 4.2.1 Triangle Congruence: SSS and SAS
  • 4.2.2 Triangle Congruence: ASA, AAS, and HL
  • 4.2.3 Triangle Congruence: CPCTC
  • 4.2.4 Introduction to Coordinate Proof
  • 4.2.5 Isosceles and Equilateral Triangles

5. Properties and Attributes of Triangles

• 5.1 Segments in Triangles
  • 5.1.1 Perpendicular and Angle Bisector Theorems
  • 5.1.2 Medians, Altitudes, and Midsegments in Triangles

• 5.2 Relationships in Triangles
  • 5.2.1 Indirect Proof and Inequalities in One Triangle
  • 5.2.2 Inequalities in Two Triangles
  • 5.2.3 The Pythagorean Theorem
  • 5.2.4 Applying Special Right Triangles

6. Polygons and Quadrilaterals

• 6.1 Polygons and Parallelograms
  • 6.1.1 Properties and Attributes of Polygons
  • 6.1.2 Properties of Parallelograms
  • 6.1.3 Conditions for Parallelograms

• 6.2 Other Special Quadrilaterals
  • 6.2.1 Properties of Special Parallelograms
  • 6.2.2 Conditions for Special Parallelograms
  • 6.2.3 Properties of Kites and Trapezoids

7. Similarity

• 7.1 Similarity Relationships
  • 7.1.1 Ratio and Proportion
  • 7.1.2 Ratios in Similar Polygons
  • 7.1.3 Triangle Similarity: AA, SSS, and SAS

• 7.2 Applying Similarity
  • 7.2.1 Applying Properties of Similar Triangles
  • 7.2.2 Using Proportional Relationships
  • 7.2.3 Dilations and Similarity in the Coordinate Plane

8. Right Triangles and Trigonometry

• 8.1 Trigonometric Ratios
  • 8.1.1 Similarity in Right Triangles
  • 8.1.2 Trigonometric Ratios
  • 8.1.3 Solving Right Triangles

• 8.2 Applying Trigonometric Ratios
  • 8.2.1 Angles of Elevation and Depression
  • 8.2.2 Law of Sines and Law of Cosines
  • 8.2.3 Vectors

9. Extending Perimeter, Circumference, and Area

• 9.1 Developing Geometric Formulas
  • 9.1.1 Developing Formulas for Triangles and Quadrilaterals
  • 9.1.2 Developing Formulas for Circles and Regular Polygons
  • 9.1.3 Composite Figures

• 9.2 Applying Geometric Formulas
  • 9.2.1 Perimeter and Area in the Coordinate Plane
  • 9.2.2 Effects of Changing Dimensions Proportionally
  • 9.2.3 Geometric Probability

10. Spatial Reasoning

• 10.1 Three-Dimensional Figures
  • 10.1.1 Solid Geometry
  • 10.1.2 Representations of Three-Dimensional Figures
  • 10.1.3 Formulas in Three Dimensions

• 10.2 Surface Area and Volume
  • 10.2.1 Surface Area of Prisms and Cylinders
  • 10.2.2 Surface Area of Pyramids and Cones
  • 10.2.3 Volume of Prisms and Cylinders
  • 10.2.4 Volume of Pyramids and Cones
  • 10.2.5 Spheres

11. Circles

• 11.1 Lines and Arcs in Circles
  • 11.1.1 Lines That Intersect Circles
  • 11.1.2 Arcs and Chords
  • 11.1.3 Sector Area and Arc Length

• 11.2 Angles and Segments in Circles
  • 11.2.1 Inscribed Angles
  • 11.2.2 Angle Relationships in Circles
  • 11.2.3 Segment Relationships in Circles
  • 11.2.4 Circles in the Coordinate Plane

12. Transformational Geometry

• 12.1 Congruence Transformations
  • 12.1.1 Reflections
  • 12.1.2 Translations
  • 12.1.3 Rotations
  • 12.1.4 Compositions of Transformations

• 12.2 Patterns
  • 12.2.1 Symmetry
  • 12.2.2 Tessellations
  • 12.2.3 Dilations

13. Appendix: Essential Algebra Review

• 13.1 Solving Equations and Inequalities
  • 13.1.1 Simplifying Expressions
  • 13.1.2 Writing and Solving Two-Step Equations
  • 13.1.3 Solving Two-Step Inequalities
  • 13.1.4 Writing and Solving Multi-Step Equations
  • 13.1.5 Solving Equations with Variables on Both Sides
  • 13.1.6 Systems of Equations

• 13.2 Graphing and the Coordinate Plane
  • 13.2.1 The Coordinate Plane
  • 13.2.2 Equations, Tables, and Graphs
  • 13.2.3 Graphing Using Intercepts

• 13.3 Ratio and Proportion
  • 13.3.1 Rates, Ratios, and Proportions
  • 13.3.2 Applications of Proportions
  • 13.3.3 Finding and Using Percents

• 13.4 Operations with Polynomials and Factoring
  • 13.4.1 Adding and Subtracting Polynomials
  • 13.4.2 Multiplying and Dividing Monomials
  • 13.4.3 Multiplying Monomials by Polynomials
  • 13.4.4 Multiplying Binomials
  • 13.4.5 Factoring with the GCF
  • 13.4.6 Factoring x² + bx + c
  • 13.4.7 Factoring ax² + bx + c

• 13.5 Radicals and Solving Quadratics
  • 13.5.1 Radical Expressions
  • 13.5.2 Solving Quadratic Equations by Factoring
  • 13.5.3 Solving Quadratic Equations by Using Square Roots