Table of Contents
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Chapter 0 Preparing for Geometry
- Converting Length: Metric Units
- Converting and Comparing Length: Customary Units
- Converting Capacity: Liters and Milliliters
- Converting and Comparing Capacity: Customary Units
- Converting and Comparing Mass: Metric Units
- Converting and Comparing Mass: Customary Units
- Converting between Metric and Customary Units of Length
- Converting between Metric and Customary Units of Capacity
- Converting between Metric and Customary Units of Mass
- Probability of Simple Events
- Writing and Evaluating Algebraic Expressions
- Evaluating Higher-Degree Algebraic Expressions
- Addition and Subtraction of Algebraic Expressions
- One-step Equations: Addition and Subtraction
- One-step Equations: Multiplication and Division
- Two-Step Equations
- Multistep Inequalities
- One-step Inequalities: Multiplication or Division
- Quadrants of the Coordinate Plane
- Solving Systems of Linear Equations Graphically
- Simplifying Radicals
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Unit 1 Geometric Structure
- Points, Lines, and Planes in Space
- Measuring to the Nearest Inch
- Congruence of Line Segments
- Centimeters
- Distance and Midpoint on a Number Line
- Distance on the Coordinate Plane: Pythagorean Formula
- Midpoint on the Coordinate Plane
- Identifying Turns and Angles
- Measuring Angles
- Angle Relationships
- Polygons
- Perimeter of a Shape
- Convex and Concave Polygons
- Area of a Triangle
- Surface Areas of Rectangular Prism and Cubes
- Patterns and Conjecture
- Laws of Deductive Reasoning
- Parallel Lines and Transversals: Angle Relationships
- Linear Functions in Different Forms
- Equation of a Straight Line: Standard and Point–Slope Forms
- Slope of a Line through Two Points
- Equation of a Straight Line: Slope–Intercept Form
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Unit 2 Congruence
- Types of Triangles: Angles and Sides
- Types of Triangles: Angles
- Applications on Congruent Triangles
- Congruence of Triangles: SSS, SAS, and RHS
- Congruence of Triangles: ASA and AAS
- Isosceles Triangles
- Equilateral Triangles
- Congruence of Polygons through Transformations
- Triangles on the Coordinate Plane
- Medians of Triangles
- Inequality in One Triangle: Angle–Side
- Inequality in One Triangle: Sides
- Interior Angles of a Polygon
- Exterior Angles of a Polygon
- Properties of Parallelograms
- Parallelograms on the Coordinate Plane
- Properties of Rectangles
- Perimeters of Rectangles and Squares
- Areas of Rectangles and Squares
- Hierarchy of Quadrilaterals
- Properties of Rhombuses
- Properties of Squares
- Properties of Kites
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Unit 3 Similarity
- Proportions
- Equivalent Ratios
- Ratios of Geometric Figures
- Similar Polygons
- Applications of Similar Polygons
- Conditions for Similar Triangles
- Parallel Lines and Transversals: Proportional Parts
- Scale Drawings and Models
- Geometric Mean
- The Pythagorean Theorem
- The Converse of the Pythagorean Theorem
- Special Right Triangles
- Trigonometric Ratios of Special Triangles
- Trigonometric Ratios in Right Triangles
- Inverse Trigonometric Functions
- Right Triangle Trigonometry: Solve for an Angle
- Angles of Elevation and Depression
- Law of Cosines
- Applications on Sine and Cosine Laws
- Vector Operations in 2D
- Vector Fields
- Components of a Vector
- Reflections on the Coordinate Plane
- Reflections of Shapes
- Geometric Translations
- Translations on a Coordinate Plane
- Rotations about a Point
- Rotations on the Coordinate Plane
- Rotational Symmetry
- Lines of Symmetry
- Combining Transformations
- Dilation: Positive Scale Factors
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Unit 4 Measurement
- Arc Lengths and Sectors
- Circumference of a Circle
- Measures of Arcs
- Central Angles in a Circle
- Special Segments in a Circle
- Perpendicular Bisector of a Chord
- Inscribed Angles in a Circle
- Angles of Tangency
- Tangents of a Circle
- Areas of Circular Segments
- Equation of a Circle
- Equation of a Circle Passing through Three Noncollinear Points
- Finding the Area of a Rhombus Using Diagonals
- Area of a Kite
- Area of a Circle
- Areas of Composite Figures
- Areas of Composite Polygons
- Areas of Regular Polygons
- Surface Areas of Prisms
- Volumes of Rectangular Prisms and Cubes
- Surface Areas of Cylinders
- Surface Areas of Pyramids
- Applications on the Pythagorean Theorem
- Volumes of Triangular Prisms
- Volumes of Composite Solids
- Volumes of Cylinders
- Volumes of Pyramids
- Volumes of Cones
- Volumes of Spheres
- Surface Areas of Spheres
- Introduction to Probability
- Using Permutations to Find Probability
- Using Combinations to Find Probability
- Geometric Probability
- Simulation Design
- Estimating Probability Using Simulations
- Mutually Exclusive Events