Geometry Companion Website

Select the chapter title below to access activities, theorems, and videos.

R. Review

• Videos
  R.1 Solving Equations

  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

  R.2 Solving Inequalities

  The Addition Property of Inequality
  The Multiplication Property of Inequality

  R.3 The Slope-Intercept Form of a Line

  Slope of a Line
  Slope and the Steepness of a Line
  Horizontal and Vertical Lines
  Graphing Equations Using Slope and Intercept

  R.4 Solving a System of Equations

  Solving by Substitution
  Solving by Elimination

  R.5 Multiplying Polynomials

  Multiplying Monomials
  Multiplying a Binomial by a Monomial
  Multiplying Polynomials
  Multiplying Binomials: FOIL
  Squares of Binomials

  R.6 Factoring Polynomials

  Factoring x² + bx + c
  Factoring a Trinomial with ax² Term, a ≠ 1
  The Zero-Product Property

  R.8 Completing the Square

  Complete the Square
  Complete the Square: a > 1
  Solving a Quadratic Equation
  Complete the Square: a < 0

  R.9 Graphing Parabolas

  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

  R.10 Area and Perimeter Fundamentals

  Area and Perimeter of Rectangles and Triangles
  Finding Area Using the Coordinate Plane
  Area and Circumference of Circles

  R.11 Pythagorean Theorem

  Pythagorean Theorem

1. Geometry Fundamentals

• Activities
  

  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

  1.5 Rotation: Angle Rotation

  1.5 Rotation: Figure Rotation

  1.6 Reflection, Rotation, and Symmetry: Segment Reflection

  1.6 Reflection, Rotation, and Symmetry: Angle Reflection

  1.6 Reflection, Rotation, and Symmetry: Figure Reflection

• Videos
  1.1 Geometry Essentials

  Points, Lines, and Planes
  More Postulates About Points, Lines, and Planes
  Angles
  Interactive Problems: Angle Action
  Construction: Copying Segments and Angles

  1.2 Measuring Distances

  The Distance Formula
  The Midpoint Formula
  Solving a Proportion

  1.3 Rates, Ratios, and Proportions

  Rigid Motion
  Congruent Triangles
  Congruent Figures

  1.4 Translation in a Coordinate Plane

  Translation in a Coordinate Plane
  Calculating the Coordinates for Translated Figures
  Activity: Translation

  1.5 Rotation

  Rotations
  Mathematics of 180° Rotations
  Mathematics of 90° Rotations
  Activity: Rotating a Figure

  1.6 Reflection, Rotation, and Symmetry

  Symmetry and Reflection
  Calculating the Coordinates of a Reflected Image
  Reflecting About a Line
  Lines of Symmetry
  Rotational Symmetry

  1.7 Composition of Transformations

  Reflections and Rotation

• Postulates & Theorems

2. Similar Figures and Dilation

• Activities
  

  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

• Videos
  2.1 Similar Figures

  Similar Triangles
  Identifying Congruent Angles

  2.2 Dilation and Similar Figures

  Dilation
  Calculating the Scale Factor
  Application: Rescaling an Image

  2.3 Similarity, Polygons, and Circles

  Similar Polygons and Circles
  Similar Polygons: More Similarities

  2.4 Similarity and Transformations

  Composition of Transformations

• Postulates & Theorems

3. Reasoning

• Activities
  

  3.3 Deductive Reasoning: Your First Proof

  3.4 Reasoning in Geometry: Angles and Their Relationship Proof

• Videos
  3.1 Inductive Reasoning

  Induction
  Finding Patterns in Numbers

  3.2 Conditional Statements

  Conditional Statements
  Applying Conditionals
  Converse, Inverse, and Contrapositive Statements
  Writing Four Related Statements
  Biconditionals
  Definitions

  3.3 Deductive Reasoning

  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

  3.4 Reasoning in Geometry

  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

• Postulates & Theorems

4. Parallel and Perpendicular Lines

• Activities
  

  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

• Videos
  4.1 Parallel Lines and Angles

  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

  4.2 More on Parallel Lines and Angles

  Proving Angle Relationships
  Find the Angle Measures Given Parallel Lines
  Theorem Converses for Parallel Lines
  Using a Parallel Line Theorem Converse

  4.3 Perpendicular Lines

  Theorems for Pairs of Perpendicular Lines
  Applying Perpendicular Theorems
  Constructing Perpendicular and Parallel Lines
  Distance and Perpendicular Lines

  4.4 Parallel Lines, Perpendicular Lines, and Slope

  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

  4.5 Parallel Lines and Triangles

  Interior and Exterior Angles
  Exterior Angle Theorem
  Angles in a Right Triangle

• Postulates & Theorems

5. Congruent Triangles

• Videos
  5.1 Isosceles and Equilateral 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

  5.2 Congruent Figures

  Third Angles Theorem
  Sample Problems: Prove Triangles Are Congruent

  5.3 Proving Triangles Congruent with SSS and SAS

  Side-Side-Side (SSS) Postulate
  Hypotenuse-Leg Theorem
  Side-Angle-Side (SAS) Postulate

  5.4 Proving Triangles Congruent with ASA and AAS

  Angle-Side-Angle (ASA) Postulate
  Congruence and Translations
  Introduction to Coordinate Proofs
  Proof: Translation Is Isometric

• Postulates & Theorems

6. Relationships Within Triangles

• Videos
  6.1 Midsegments

  Midsegments
  Another Midsegment Theorem

  6.2 Perpendicular and Angle Bisectors

  Perpendicular Bisectors
  Angle Bisector Theorem and Converse
  Applying an Angle Bisector Theorem

  6.3 Circumcenters

  Perpendicular Bisectors in a Triangle

  6.4 Centroids and Orthocenters

  Medians in a Triangle
  Altitudes in a Triangle

  6.5 Incenters

  Angle Bisectors in a Triangle
  Summary of Circumcenters, Incenters, Centroids, and Orthocenters

  6.6 Optional: Inequalities in One Triangle

  Inequalities of Sums of Triangle Sides
  Applying a Triangle Inequality
  The Hinge Theorem and Its Converse

  6.7 Optional: Indirect Reasoning

  Writing an Indirect Proof

• Postulates & Theorems

7. Similarity and Trigonometry

• Activities
  

  7.6 Trigonometric Ratios: Sine, Cosine, and Tangent in Right Triangles

  7.8 Law of Cosines and Law of Sines: Alien Spacecraft

• Videos
  7.1 Similarity: Angle-Angle and Side-Side-Side

  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

  7.2 Similar Triangles: Side-Angle-Side Theorem

  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

  7.4 Similar Right Triangles

  Similar Right Triangles
  Converse of Pythagorean Theorem
  Classifying Triangles Using the Pythagorean Theorem

  7.5 Special Right Triangles

  Applying Special Right Triangles
  Application: Baseball Diamond

  7.6 Trigonometric Ratios

  Sine, Cosine, and Tangent Ratios
  Working with Sine, Cosine, and Tangent
  Using a Calculator in Trigonometry
  Sine, Cosine, and Tangent for Special Triangles

  7.7 Optional: Inverses of Trigonometric Functions

  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

• Postulates & Theorems

8. Circles

• Activities
  

  8.4 More on Chords and Angles: Chord Segment Lengths

  8.5 Arc Lengths and Area: Converting Degrees to Radians and Vice Versa

• Videos
  8.1 Circles, Tangents, and Secants

  Circles, Segments, and Lines
  Finding a Circle's Radius from a Tangent
  Application: Earth's Horizon
  Constructing Circles Based on Triangles

  8.2 Chords and Arcs

  Arc Measure
  Chord Theorems

  8.3 Inscribed Figures

  Arcs and Inscribed Angles
  Inscribed Angles That Intercept the Same Arc
  Inscribed Right Angles

  8.4 More on Chords and Angles

  Tangent, Chord, and a Circle
  Secant, Tangent, and a Circle
  Chord Lengths in Circles

  8.5 Arc Lengths and Area

  Calculating Arc Lengths

• Postulates & Theorems

9. Polygons

• Videos
  9.1 Parallelograms and Their Diagonals

  Polygons
  Calculating Where Diagonals Intersect

  9.2 Deciding If a Parallelogram Is Also a Rectangle, Square, or Rhombus

  Using a Proof to Decide If a Parallelogram Is Also a Rectangle
  Classify a Parallelogram

  9.3 Deciding If a Quadrilateral Is 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

  9.5 Trapezoids and Kites

  Trapezoids
  Isosceles Trapezoids
  Midsegments and Trapezoids
  Kites

  9.6 Areas and the Coordinate Plane

  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

  9.7 Area of Regular Polygons

  Calculating Regular Polygon Areas

  9.8 Area and Trigonometry

  Trigonometry and Regular Polygons

• Postulates & Theorems

10. Solids

• Videos
  10.1 Three-Dimensional Figures, Cross-Sections, and Drawings

  Euler's Theorem

  10.2 Surface Area

  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

  10.3 Volume

  Volume of a Rectangular Prism
  Volume of a Cylinder
  Volume of a Cone
  Volume of a Sphere

  10.4 Cavalieri's Principle

  Cavalieri's Principle
  Deriving the Volume of a Hemisphere and Sphere

  10.5 Similar Solids

  Congruent Solids
  Determining If Two Solids Are Similar
  Surface Areas and Volumes of Similar Solids

• Postulates & Theorems

11. Conics

• Activities
  

  11.2 Parabolas at the Origin: Focus and Directrix of a Parabola

  11.2 Parabolas at the Origin: Graphing the Standard Form of the Equation for a Parabola at the Origin

  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

  11.4 Optional: Parabolas Translated from the Origin: Properties of a Parabola Translated 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

• Videos
  11.1 Circles at the Origin

  Circles Centered at the Origin
  Sample Problems: Circles

  11.2 Parabolas at the Origin

  Geometric Definition of a Parabola
  Graphing a Parabola at the Origin
  Sample Problem: Determining the Equation of a Parabola

  11.3 Circles Translated from the Origin

  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

  11.4 Optional: Parabolas Translated from the Origin

  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

  11.5 Ellipses at the Origin

  Ellipses
  Ellipses Centered at the Origin
  The Vertices, Axes, and Center of an Ellipse
  Rewriting an Equation of an Ellipse in Standard Form

  11.6 Hyperbolas at the Origin

  Geometric Definition of a Hyperbola
  Graphing a Hyperbola
  Writing an Equation for a Hyperbola

12. Probability

• Activities
  

  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

• Videos
  12.1 Introduction to Probability

  Graphing a Sample Space
  Application: Modeling Populations
  Expected Value and Mean of a Probability Distribution

  12.3 Independent Events and the Multiplication Rule

  Probability Simulation and Compound Events