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Congruence, Proof, and Constructions
- Definitions of Geometric Objects
- Transformations and Rigid Motions of Figures
- Symmetries of Plane Figures
- Rotations of Figures in a Plane
- Translations of Figures in a Plane
- Reflections of Figures in a Plane
- Rigid Motion and Congruence
- Congruent Triangles
- Criteria for Triangle Congruence
- Theorems About Lines and Angles
- Theorems About Triangles
- More Theorems About Triangles
- Theorems About Parallelograms
- Compass and Straight Edge Constructions
- Constructions Using Different Tools
- Polygons Inscribed in a Circle
Similarity, Proof, and Trigonometry
- Dilation and Scale Factor
- Understanding Similarity Transformations
- The Conditions for Triangle Similarity
- Similarity Theorems About Triangles
- Application of Congruence and Similarity Theorems
- Trigonometric Ratios of Acute Angles
- Properties of the Trigonometric Ratios
- Application of Trigonometric Ratios
- Modeling Using Geometric Shapes
- Modeling Using Area and Volume
- Geometry in Design
- Sine and the Area of a Triangle
- Solving Triangles Using the Law of Sines
- Solving Triangles Using the Law of Cosines
- Application of the Laws of Sine and Cosine
Extending to Three Dimensions
- Area and Volume Scale Factors
- Properties of Cylinders
- Properties of Cones
- Properties of Pyramids
- Properties of Spheres
- The Rotation of Two Dimensional Geometric Objects
- Modeling in Three Dimensions
Connecting Algebra and Geometry Through Coordinates
- Using the Distance and Midpoint Formulas in Proofs
- Slope of Parallel and Perpendicular Lines
- Position of Points on a Line Segment
- Perimeter and Area in a Coordinate Plane
- The Focus and Directrix of Parabolas
Circles With and Without Coordinates
- Proving the Similarity of All Circles
- Circle Theorems
- Inscribed and Circumscribed Circles of a Triangle
- Quadrilaterals Inscribed in a Circle
- Tangent Line to a Circle
- Radian Measure and Arc Length
- Area of a Sector
- Equation of a Circle
- Using Coordinates in Proofs
- Modeling With Circles
Applications of Probability
- The Basics of Event Probability
- Probability and the Independence of Events
- The Relationship Between Independence and Conditional Probability
- Conditional Probability in the Uniform Probability Model
- Probability in Length, Area, and Volume
- Constructing and Interpreting Two-Way Frequency Tables
- Recognizing Independence and Making Decisions
- Addition Rule in the Uniform Probability Model
- Multiplication Rule in the Uniform Probability Model
- Permutations and Combinations in Probability
- Making Fair Decisions
- Examining Decisions