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Geometry

UNIT.1  Constructions and Rigid Transformations

Constructions

  • Build It
  • Constructing Patterns
  • Construction Techniques 1: Perpendicular Bisectors
  • Construction Techniques 2: Equilateral Triangles
  • Construction Techniques 3: Perpendicular Lines and Angle Bisectors
  • Construction Techniques 4: Parallel and Perpendicular Lines
  • Construction Techniques 5: Squares
  • Using Technology for Constructions
  • Speedy Delivery

Rigid Transformations

  • Rigid Transformations
  • Defining Reflections
  • Defining Translations
  • Incorporating Rotations
  • Defining Rotations
  • Symmetry
  • More Symmetry
  • Working with Rigid Transformations
  • Practicing Point by Point Transformations

Evidence and Proof

  • Evidence, Angles, and Proof
  • Transformations, Transversals, and Proof

UNIT.2  Congruence

Congruent Triangles

  • Congruent Parts, Part 1
  • Congruent Parts, Part 2
  • Congruent Triangles, Part 1
  • Congruent Triangles, Part 2
  • Points, Segments, and Zigzags
  • Side-Angle-Side Triangle Congruence
  • Angle-Side-Angle Triangle Congruence
  • The Perpendicular Bisector Theorem
  • Practicing Proofs
  • Side-Side-Angle (Sometimes) Congruence

Proofs about Quadrilaterals

  • Proofs about Quadrilaterals
  • Proofs about Parallelograms
  • Bisect It

UNIT.3  Similarity

Properties of Dilations

  • Scale Drawings
  • Scale of the Solar System
  • Measuring Dilations
  • Dilating Lines and Angles
  • Splitting Triangle Sides with Dilation, Part 1

Similarity Transformations and Proportional Reasoning

  • Connecting Similarity and Transformations
  • Reasoning about Similarity with Transformations
  • Are They All Similar?
  • Conditions for Triangle Similarity
  • Other Conditions for Triangle Similarity
  • Splitting Triangle Sides with Dilation, Part 2
  • Practice With Proportional Relationships

Similarity in Right Triangles

  • Using the Pythagorean Theorem and Similarity
  • Proving the Pythagorean Theorem
  • Finding All the Unknown Values in Triangles

UNIT.4  Right Triangle Trigonometry

Angles and Steepness

  • Angles and Steepness
  • Half a Square
  • Half an Equilateral Triangle
  • Ratios in Right Triangles
  • Working with Ratios in Right Triangles

Defining Trigonometric Ratios

  • Working with Trigonometric Ratios
  • Applying Ratios in Right Triangles
  • Sine and Cosine in the Same Right Triangle
  • Using Trigonometric Ratios to Find Angles
  • Solving Problems with Trigonometry
  • Approximating Pi

UNIT.5  Solid Geometry

Cross Sections, Scaling, and Area

  • Solids of Rotation
  • Slicing Solids
  • Creating Cross Sections by Dilating
  • Scaling and Area
  • Scaling and Unscaling

Scaling Solids

  • Scaling Solids
  • The Root of the Problem
  • Speaking of Scaling

Prism and Cylinder Volumes

  • Cylinder Volumes
  • Cross Sections and Volume
  • Prisms Practice

Understanding Pyramid Volumes

  • Prisms and Pyramids
  • Building a Volume Formula for a Pyramid
  • Working with Pyramids
  • Putting All the Solids Together
  • Surface Area and Volume
  • Volume and Density
  • Volume and Graphing

UNIT.6   Coordinate Geometry

Transformations in the Plane

  • Rigid Transformations in the Plane
  • Transformations as Functions
  • Types of Transformations

Distances, Circles, and Parabolas

  • Distances and Circles
  • Squares and Circles
  • Completing the Square
  • Distances and Parabolas
  • Equations and Graphs

Proving Geometric Theorems Algebraically

  • Equations of Lines
  • Parallel Lines in the Plane
  • Perpendicular Lines in the Plane
  • It’s All on the Line
  • Intersection Points
  • Coordinate Proof
  • Weighted Averages
  • Weighted Averages in a Triangle
  • Lines in Triangles

UNIT.7   Circles

Lines, Angles, and Circles

  • Lines, Angles, and Curves
  • Inscribed Angles
  • Tangent Lines

Polygons and Circles

  • Quadrilaterals in Circles
  • Triangles in Circles
  • A Special Point
  • Circles in Triangles

Measuring Circles

  • Arcs and Sectors
  • Part to Whole
  • Angles, Arcs, and Radii
  • A New Way to Measure Angles
  • Radian Sense
  • Using Radians

UNIT.8   Conditional Probability

Up to Chance

  • Up to Chance
  • Playing with Probability
  • Sample Spaces
  • Tables of Relative Frequencies

Combining Events

  • Combining Events
  • The Addition Rule

Related Events

  • Related Events
  • Conditional Probability
  • Using Tables for Conditional Probability
  • Using Probability to Determine Whether Events Are Independent

Conditional Probability

  • Probabilities in Games
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