R. Review
Addition Property of Equality
Multiplication Property of Equality
Combining Like Terms to Solve an Equation
Solving for a Variable
Writing a Ratio
What Is a Proportion?
Application: Estimating Wildlife Populations
The Addition Property of Inequality
The Multiplication Property of Inequality
Slope of a Line
Slope and the Steepness of a Line
Horizontal and Vertical Lines
Graphing Equations Using Slope and Intercept
Solving by Substitution
Solving by Elimination
Multiplying Monomials
Multiplying a Binomial by a Monomial
Multiplying Polynomials
Multiplying Binomials: FOIL
Squares of Binomials
Factoring x² + bx + c
Factoring a Trinomial with ax² Term, a ≠ 1
The Zero-Product Property
Complete the Square
Complete the Square: a > 1
Solving a Quadratic Equation
Complete the Square: a < 0
Graphing a Parabola
Graphing a Parabola of the Form f(x) = ax²
Solving Quadratic Equations Graphically
Finding the x-intercepts of a Parabola
Translating a Parabola Vertically
Translating a Parabola Horizontally
Area and Perimeter of Rectangles and Triangles
Finding Area Using the Coordinate Plane
Area and Circumference of Circles
1. Geometry Fundamentals
1.3 Transformations and Congruent Figures: Angle Translation
1.4 Translation in a Coordinate Plane: Gnome Translation
1.4 Translation in a Coordinate Plane: Monster Translation
1.4 Translation in a Coordinate Plane: Mouse Translation
1.5 Rotation: Segment Rotation
1.6 Reflection, Rotation, and Symmetry: Segment Reflection
Points, Lines, and Planes
More Postulates About Points, Lines, and Planes
Angles
Interactive Problems: Angle Action
Construction: Copying Segments and Angles
The Distance Formula
The Midpoint Formula
Solving a Proportion
Rigid Motion
Congruent Triangles
Congruent Figures
Translation in a Coordinate Plane
Calculating the Coordinates for Translated Figures
Activity: Translation
Rotations
Mathematics of 180° Rotations
Mathematics of 90° Rotations
Activity: Rotating a Figure
Symmetry and Reflection
Calculating the Coordinates of a Reflected Image
Reflecting About a Line
Lines of Symmetry
Rotational Symmetry
2. Similar Figures and Dilation
2.2 Dilation and Similar Figures: Vertical Dilation
2.2 Dilation and Similar Figures: Horizontal Dilation
2.2 Dilation and Similar Figures: Positive Slope
2.2 Dilation and Similar Figures: Negative Slope
2.2 Dilation and Similar Figures: Line Through Origin
2.3 Similarity, Polygons, and Circles: Working with Buildings
2.3 Similarity, Polygons, and Circles: Working with Pyramids
Similar Triangles
Identifying Congruent Angles
Dilation
Calculating the Scale Factor
Application: Rescaling an Image
Similar Polygons and Circles
Similar Polygons: More Similarities
3. Reasoning
3.3 Deductive Reasoning: Your First Proof
3.4 Reasoning in Geometry: Angles and Their Relationship Proof
Induction
Finding Patterns in Numbers
Conditional Statements
Applying Conditionals
Converse, Inverse, and Contrapositive Statements
Writing Four Related Statements
Biconditionals
Definitions
Deductive Reasoning
Using Mathematical Properties to Write a Geometric Proof
Sample Problem: Angles and Algebra
Applying Reasoning Skills to Solve an Equation
Diagrams and Postulates
Angles and Their Relationships
Vertical Angles
Sample Problem: Vertical and Supplementary Angles
Properties of Equality and Congruence
Proof of Vertical Angles Congruence Theorem
Reasoning and Graphs
4. Parallel and Perpendicular Lines
4.1 Parallel Lines and Angles: Prove the Alternate Interior Angles Theorem
4.2 More on Parallel Lines and Angles: Prove the Alternate Exterior Angles Theorem
Parallel and Perpendicular Lines
Corresponding Angles
Using the Corresponding Angles Postulate
Alternative Interior and Exterior Angles
Sample Problem: Using Angle Relationships and a Transversal
Consecutive Interior Angles
Proving Angle Relationships
Find the Angle Measures Given Parallel Lines
Theorem Converses for Parallel Lines
Using a Parallel Line Theorem Converse
Theorems for Pairs of Perpendicular Lines
Applying Perpendicular Theorems
Constructing Perpendicular and Parallel Lines
Distance and Perpendicular Lines
Determining When Lines Are Parallel
Determining When Lines Are Perpendicular
Using Line Relationships to Write Equations
Slope and Right Triangles
Distance Between a Point and a Line
Interior and Exterior Angles
Exterior Angle Theorem
Angles in a Right Triangle
5. Congruent Triangles
Types of Triangles
Sample Problem: Determining the Type of Triangle
Sample Problem: A Triangle and the Distance Formula
Additional Isosceles Triangle Theorems
Equilateral Triangle Theorems
Constructing an Equilateral Triangle
Third Angles Theorem
Sample Problems: Prove Triangles Are Congruent
Side-Side-Side (SSS) Postulate
Hypotenuse-Leg Theorem
Side-Angle-Side (SAS) Postulate
Angle-Side-Angle (ASA) Postulate
Congruence and Translations
Introduction to Coordinate Proofs
Proof: Translation Is Isometric
6. Relationships Within Triangles
Midsegments
Another Midsegment Theorem
Perpendicular Bisectors
Angle Bisector Theorem and Converse
Applying an Angle Bisector Theorem
Perpendicular Bisectors in a Triangle
6.4 Centroids and Orthocenters Medians in a Triangle
Altitudes in a Triangle
Angle Bisectors in a Triangle
Summary of Circumcenters, Incenters, Centroids, and Orthocenters
Inequalities of Sums of Triangle Sides
Applying a Triangle Inequality
The Hinge Theorem and Its Converse
7. Similarity and Trigonometry
7.6 Trigonometric Ratios: Sine, Cosine, and Tangent in Right Triangles
The Angle-Angle (AA) Similarity Postulate
Sample Problem: Similar Triangles with a Shared Angle
Side-Side-Side (SSS) Similarity Theorem
Sample Problem: Checking for Similar Triangles
Application: Height of a Tower
Side-Angle-Side (SAS) Similarity Theorem
7.3 Pythagorean Theorem Pythagorean Theorem
Proving the Pythagorean Theorem
Finding the Area of an Isosceles Triangle
Formula for Pythagorean Triples
Similar Right Triangles
Converse of Pythagorean Theorem
Classifying Triangles Using the Pythagorean Theorem
Applying Special Right Triangles
Application: Baseball Diamond
Sine, Cosine, and Tangent Ratios
Working with Sine, Cosine, and Tangent
Using a Calculator in Trigonometry
Sine, Cosine, and Tangent for Special Triangles
Inverses of the Trigonometric Functions
7.8 Law of Cosines and Law of Sines The Law of Cosines and Solving SAS and SSS Triangles
The Law of Sines and Solving ASA and AAS Triangles
8. Circles
8.4 More on Chords and Angles: Chord Segment Lengths
8.5 Arc Lengths and Area: Converting Degrees to Radians and Vice Versa
Circles, Segments, and Lines
Finding a Circle's Radius from a Tangent
Application: Earth's Horizon
Constructing Circles Based on Triangles
Arcs and Inscribed Angles
Inscribed Angles That Intercept the Same Arc
Inscribed Right Angles
Tangent, Chord, and a Circle
Secant, Tangent, and a Circle
Chord Lengths in Circles
9. Polygons
Polygons
Calculating Where Diagonals Intersect
Using a Proof to Decide If a Parallelogram Is Also a Rectangle
Classify a Parallelogram
Quadrilaterals and Parallelograms: Theorem Converses
9.4 Optional: Polygons and Their Angles Polygons and Their Interior Angles
Measure of an Angle in a Polygon
Using Interior Angles
Exterior Angles of a Convex Polygon
Trapezoids
Isosceles Trapezoids
Midsegments and Trapezoids
Kites
Area of Rhombus
Area of Parallelogram in Coordinate Plane
Area of Rectangle in Coordinate Plane
Area of a Triangle in Coordinate Plane
Area of a Trapezoid
Calculating a Base in a Trapezoid
Calculating the Length of a Diagonal
10. Solids
Surface Area of a Cube
Using Nets to Find Surface Area
Surface Area of a Prism
Surface Area of a Cylinder
Surface Area of a Pyramid
Surface Area of a Cone
Surface Area of a Sphere
Volume of a Rectangular Prism
Volume of a Cylinder
Volume of a Cone
Volume of a Sphere
Cavalieri's Principle
Deriving the Volume of a Hemisphere and Sphere
Congruent Solids
Determining If Two Solids Are Similar
Surface Areas and Volumes of Similar Solids
11. Conics
11.2 Parabolas at the Origin: Focus and Directrix of a Parabola
11.2 Parabolas at the Origin: Graph a Parabola Using the Focus and Directrix
11.4 Optional: Parabolas Translated from the Origin: Translating a Parabola from the Origin
11.5 Elipses at the Origin: Foci of an Ellipse
11.5 Ellipses at the Origin: Properties of an Ellipse
11.6 Hyperbolas at the Origin: Vertices and Foci of a Hyperbola
11.6 Hyperbolas at the the Origin: Properties of a Hyperbola
Circles Centered at the Origin
Sample Problems: Circles
Geometric Definition of a Parabola
Graphing a Parabola at the Origin
Sample Problem: Determining the Equation of a Parabola
Circles Not Centered at the Origin
Graphing a Circle Translated from the Origin
Rewriting an Equation of a Circle in Standard Form
Completing the Square to Write an Equation of a Circle in Standard Form
The Standard Form of the Equation for a Parabola
Sample Problem: Graphing a Parabola in Standard Form
Sample Problem: Writing an Equation for a Parabola from Its Graph
Rewriting an Equation of a Parabola in Standard Form
Ellipses
Ellipses Centered at the Origin
The Vertices, Axes, and Center of an Ellipse
Rewriting an Equation of an Ellipse in Standard Form
Geometric Definition of a Hyperbola
Graphing a Hyperbola
Writing an Equation for a Hyperbola
12. Probability
12.1 Introduction to Probablity: Three Coins Tossed
12.1 Introduction to Probablity: Four Coins Tossed
12.1 Introduction to Probablity: Six Coins Tossed
12.1 Introduction to Probablity: Sixteen Coins Tossed
12.1 Introduction to Probablity: Millionaire Game Round 1
12.1 Introduction to Probability: Aardvark Game
12.3 Independent Events and the Multiplication Rule: Millionaire Game Round 2
Graphing a Sample Space
Application: Modeling Populations
Expected Value and Mean of a Probability Distribution