Geometry Collected Resources

Dr. Jack L. Jackson II, Jan 31, 2022

This GeoGebra book collects activities for use in the study of Geometry. It includes all of the public activities written by Dr. Jackson along with some of the best activities written and made publicly available by other mathematics educators. This collection includes activities used with Dr. Jackson's College Geometry course. In that course, he works simultaneously in Taxicab, Hyperbolic, and Spherical Geometry along with the traditional Euclidean Geometry. In particular, Dr. Jackson has created two activities: Spherical Geometry Environment and Unified Geometry Environment. The Spherical Geometry Environment has custom tools for working in Spherical Geometry. The Unified Geometry Environment has tools for working in Euclidean, Taxicab, and Hyperbolic Geometries. The model used for Hyperbolic Geometry is the Beltrami-Poincare Half-plane model. These environments have non-Euclidean versions of all of the built-in Euclidean Geometry tools. Be sure to open them in the app to have access to the tools. Because of the number of custom tools, these files may open slowly. While this collection includes some activities for a more advanced course, most of these activities are also appropriate for a high school course in Geometry and some are appropriate for elementary and middle level students..

Table of Contents

  1. 1. Some GeoGebra Basics
    1. Drawing vs. Constructing, The Drag Test
  2. 2. Basic Unified Geometry Environments
    1. Unified Geometry Environment
    2. Spherical Geometry Environment
    3. Unified Geometry Environment B
  3. 3. Introducing Multiple Geometries
    1. Spherical Geometry Environment
    2. Unified Geometry Environment
    3. Hyperbolic Geometry: The Poincare Disk Model
  4. 4. Distance and Order
    1. Naming Points, Segments, Rays, and Lines
    2. Naming Geometric Objects
    3. Centimeter Ruler: Custom Templates
    4. Quiz: Distance in the Coordinate Plane (V1)
    5. Euclidean and Taxicab Distance
    6. AQR Section 37: Taxicab Distance v. Euclidean Distance
    7. Hyperbolic Distance Metric
  5. 5. Angles
    1. Discovering Ways to Name Angles
    2. Naming Angles
    3. Measuring Angles Using a Protractor
    4. Drawing Angles Using a Protractor
    5. Naming Angles According to Their Size
    6. Creating Angles on a Grid
    7. Identifying Angles Around Us
    8. Determining Angle Measures Without Tools
    9. Drawing Angles: Hot and Cold Activity
    10. Drawing Angles Game
    11. Creating Angles on a Grid
    12. Congruent Angles: Definition
    13. Vertical Angles Exploration (2)
    14. Vertical Angles Theorem
    15. Vertical Angles
    16. Adjacent Angles
    17. Finding the Missing Angle
    18. Complementary and Supplementary Angles
    19. Unknown Complementary Angles
    20. Supplementary Angles (Quick Exploration)
    21. Drawing Parallel, Perpendicular, and Intersecting Lines
  6. 6.A. Triangles in Euclidean Geometry
    1. Euclidean General Triangle measured
    2. Classifying Triangles in Euclidean Geometry
    3. Exploring Types of Triangles
    4. Drawing Triangles
    5. Isosceles Triangles in Euclidean,. Hyperbolic, and Taxicab
    6. Definition of Congruent Triangles
    7. Triangle Congruence
    8. SAS Triangle Congruence Exploration Euclidean Geometry
    9. SAS: Dynamic Proof!
    10. ASA Triangle Congruence Exploration Euclidean Geometry
    11. ASA Triangle Congruence Theorem Proof
    12. ASA Theorem?
    13. SSS Triangle Congruence Exploration Euclidean Geometry
    14. SSS: Dynamic Proof!
    15. Drawing Triangles
    16. Visualizing Triangles
    17. Compass and Straightedge Constructions
    18. Exterior Angle Inequality Proof with Euclidean Illustration
    19. Triangle Exterior Angle
    20. AAS Triangle Congruence Exploration Euclidean Geometry
    21. Angle-Angle-Side (AAS): Quick Exploration
    22. SSA Triangle Congruence Exploration Euclidean Geometry
    23. SSA Theorem?
    24. AAA Triangle Exploration Euclidean Geometry
    25. Sum of Interior Angles of a Triangle
    26. Triangle Angle Theorems
    27. Triangle Solver
    28. Open Middle: Triangle Angles
    29. Shortest Distance Theorem
    30. Triangle Centers (Euclidean and Hyperbolic Geometry)
    31. Triangle Fact (I)
    32. 9 Point Circle Action
    33. Pythagorean Animation
    34. Pythagorean Theorem Animation
    35. Finding the Distance Between Two Points Using the Pythagorean Theorem
    36. Identifying Right Triangles Using the Pythagorean Theorem
  7. 6b. Triangles in Hyperbolic Geometry
    1. Hyperbolic General Tiangle Measured
    2. SAS Exploration Hyperbolic Geometry
    3. ASA Exploration Hyperbolic Geometry
    4. Exterior Angle Inequality Proof Hyperbolic Geometry
    5. AAS Exploration Hyperbolic Geometry
    6. SSS Investigation Hyperbolic Geometry
    7. SSA Exploration Hyperbolic Geometry
    8. AAA Exploration Hyperbolic Geometry
    9. Triangle Centers (Euclidean and Hyperbolic Geometry)
  8. 6.C. Triangles in Spherical Geometry
    1. General Triangle in Spherical Geometry
    2. Isosceles Triangle in Spherical Geometry
    3. SAS Exploration Spherical Geometry
    4. ASA Exploration Spherical Geometry
    5. Exterior Angle Inequality Spherical Geometry
    6. AAS Exploration Spherical Geometry
    7. AAS, AASS Counterexample in Spherical Geometry
    8. SSS Exploration Spherical Geometry
    9. SSA Exploration Spherical Geometry
    10. AAA Exploration Spherical Geometry
  9. 6.D. Triangles in Taxicab Geometry
    1. Taxicab General Triangle
    2. Euclidean Rotation in Taxicab Geometry
    3. SAS Exploration Taxicab Geometry
    4. ASA and AAS Exploration Taxicab Geometry
    5. SSS Exploration Taxicab Geometry
    6. SSA Exploration Taxicab Geometry
    7. AA(A) Exploration Taxicab Geometry
    8. Taxicab Congruent Triangle Counterexamples
  10. 7. Parallel Lines
    1. Transversal to Parallel Lines
    2. Transversal Intersects Parallel Lines
    3. Alternate Interior Angles Theorem (V1)
    4. Same Side Interior Angles Theorem
    5. Exploring Alternate Exterior Angles (V2)
    6. Exploring Same Side Exterior Angles
    7. Vertical Angles Formed by Parallel Lines and a Transversal
    8. Alternate Angles Formed by Parallel Lines and a Transversal
    9. Corresponding Angles Formed By Parallel Lines and a Transversal
    10. Supplementary Angles Formed by Parallel Lines and a Transversal
    11. Parallel Lines & Related Angles
    12. Identifying Parallel Lines Cut by a Transversal
  11. 8. Quadrilaterals
    1. Classification of Quadrilaterals in Euclidean Geometry
    2. Quadrilateral Angle Theorems
    3. Convex quadrilaterals
    4. Classifying Quadrilaterals
    5. Drawing Quadrilaterals Using Properties
    6. Quadrilaterals
    7. Mystery Quadrilaterals
    8. Quadrilateral Angle Theorems
    9. Convex vs. Concave
    10. Quadrilateral Creation Templates
    11. Kite Action!
    12. Kite Template with Investigation Questions
    13. Kite in Hyperbolic Geometry
    14. Kites in Spherical Geometry
    15. Kites in Taxicab Geometry
    16. Parallelogram: Theorem 2
    17. Parallelogram: Theorem (3)
    18. Parallelograms (I)
    19. Trapezoid Median (Midsegment) Action!
    20. Trapezoid Median: 2 Discoveries
    21. Isosceles Trapezoid Template (Scaffolded Discovery)
    22. Isosceles Trapezoid Action!
    23. Concave Quadrilateral Craziness! (GoGeometry Action 80)
    24. Concave Quadrilateral Craziness! (GoGeometry Action 80)
    25. Rhombus Action!
    26. Quadrilateral Surprise!
    27. Quad Midpoints Action!
    28. Isosceles Trapezoid Midpoints
    29. Compass and Straightedge Constructions
    30. Cyclic Quadrilateral: Proof Hint
    31. Cyclic Quadrilaterals (IAT: Corollary 3)
    32. Quadrilateral "Guess Who?"
    33. Square + Rhombus = Constant Surprise! (GoGeometry Action 71)
    34. Rotational Symmetry of Quadrilaterals
    35. Japanese Theorem for Cyclic Quadrilaterals
    36. Quadrilateral Creation Templates
    37. Quadrilateral: Exterior Angles
    38. Quadrilateral Surprise!
    39. Cyclic Quadrilaterals (IAT: Corollary 3)
    40. MIdline Quadrilateral 1
  12. 9. Polygons
    1. Naming Polygons
    2. Parts of a Polygon
    3. Sum of Interior Angles of a Polygon
    4. Finding the Missing Angle of a Polygon
    5. Polygons: Exterior Angles - REVAMPED
    6. Property of cyclic polygon
    7. Pentagon Angle Theorems
  13. 10. Similarity
    1. SAS Triangle Similarity Theorem
    2. SSS Triangle Similarity Theorem
    3. Similar Triangles or Not
    4. Parallel Lines Proportionality Theorem
    5. Similar Right Triangles (V2)
    6. Triangle Midsegment Action!
    7. Making Similar Triangles
    8. Harmonic Mean In an Isosceles Trapezoid
    9. Identifying and Measuring Corresponding Sides of Similar Figures
    10. Changing Scale Factor
    11. Calculating Scale Factors of Similar Figures
    12. Corresponding Parts of Similar Figures
    13. Two Transversals to Multiple Parallel Lines
    14. Triangle Midlines, Medians, and Centroid
    15. MIdline Quadrilateral 1
    16. 2 Noncongruent Triangles with 5 Congruent Parts
  14. 11. Circle Theorems
    1. Circle with Related Figures
    2. Circumference = ? (Animation)
    3. Equidistant Chord Action
    4. Equidistant Chords, Tangent Lines
    5. Where to Sit? (I)
    6. Inscribed Angle
    7. Inscribed Angles Investigation (Revamped)
    8. Inscribed Angle Theorem (V1)
    9. Inscribed Angle Theorem: Corollary 1
    10. Angle Formed by 2 Chords (I)
    11. Crossing Chords: Proof Hint
    12. Intersecting Secant Lines to a Circle
    13. Angle From 2 Secants (V2)
  15. 12. Perimeter, Area
    1. Areas of Parallelograms and Triangles
    2. Parallelogram: Area
    3. Area of a Triangle (Discovery)
    4. Triangle Area Action!!! (V2)
    5. Triangle Area Action! (V1)
    6. Area of a Kite
    7. Area of a Rhombus
    8. Area of a Trapezoid (Discovery)
    9. Area of a Trapezoid
    10. Trapezoid: Area (I)
    11. Trapezoid: Area (2)
    12. Area of a Trapezoid (3)
    13. Trapezoid Median: 2 Discoveries
    14. Obvious Trapezoid Theorem?
    15. Circle Area (By Peeling!)
    16. Proof Without Words
    17. Pythagorean Theorem Animation
    18. Pythagorean Animation
    19. Euclid's Proof of the Pythagorean Theorem
    20. Geometric Mean Illustration
    21. Circle Area (by Peeling)
    22. Area of a Circle: Revamped!
    23. Visualizing the Area of a Circle and its Formula
    24. Pyramids in Prism
  16. 13 Miscellaneous
    1. Finding the Treasure on the Coordinate Plane
    2. GeoGebra Pentominoes
    3. Hangman hexomino cube nets
    4. Napoleon Tiling
    5. Rhombitrihexagonal Tiling
  17. 14. Volume, 3D Geometry
    1. Volume: Intuitive introduction volume of a cuboid
    2. Folding and Unfolding a Net
    3. Cube/Prism Net by List of Rotations over the edges
    4. Tetrahedron: Exploration Template
    5. Net of Polygonal Pyramid
    6. Volume of pyramid is 1/3 volume of cube (Method II )
    7. Voluem of Pyramid ( Method I )
    8. Volume of a Pyramid Using Prism
    9. Devide a cube into pyramids
    10. Cavalieri's Principle
    11. Net of an Octahedron
    12. Net of a Dodecahedron
    13. Icosahedron Net study
    14. Net of a Cone
    15. Rhombicuboctahedron's net
    16. Images. Polyhedrons and their truncated, critical truncated polyhedra
    17. Nets of Right Prisms
    18. Unfolding Shapes in 3D
    19. Square Pyramid: Underlying Anatomy
    20. Cone Anatomy
    21. Rectangular Prism: Basic Net Demo
    22. Build Your Own Right Triangular Prism (V2)!
    23. Making Cross Sections of a Prism
    24. Making Cross Sections of a Pyramid
    25. Making Cross Sections of a Sphere
    26. Making Cross Sections of a Cone
    27. Making Cross Sections of a Cylinder
    28. cilinderprojectie Gall
  18. 15. Transformations
    1. Translating Figures
    2. Angle Measures of Translated Figures
    3. Translating Points to Translate Figures
    4. Transformations: Exercise 1
    5. Reflecting a Polygon Across Axes
    6. Drawing Symmetrical Polygons
    7. Creating Your Own Robe Design with Symmetry
    8. Visualizing Lines of Symmetry
    9. Symmetric Patterns in Nature
    10. Rotations: Introduction
    11. Rotating Points Around the Origin
    12. Mapping a Triangle to a Congruent Triangle Using Reflections
    13. Identifying Congruent Figures Using Transformations
    14. Exploring a Sequence of Transformations Level 3
    15. Transformations Practice 2 (Level 1)
    16. Transformations Practice 2 (Level 2)
    17. Transformations Practice 2 (Level 3)
    18. Transformations Challenge
    19. Identifying the Type of Isometry
    20. Properties of Dilations
    21. Transformation matrices
    22. Möbius transformation
    23. Möbius transformation
    24. Transforming Points on the Coordinate Plane
    25. Writing Algebraic Rules for Transformations
    26. Proving Triangles Similar (3)
    27. AA Similarity Theorem

1.

1. Some GeoGebra Basics

These are some introductory resources for getting started with GeoGebra and learning how to use using basic tools.

  • 1. Drawing vs. Constructing, The Drag Test

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2. Basic Unified Geometry Environments

These files provide environments for Spherical, Hyperbolic, Taxicab, and Euclidean Geometry. They include custom tools for working with the non-Euclidean geometries in the same way that the built-in tools work with Euclidean Geometry. Because of the number of custom tools, these files may open slowly. Be sure to open them in the app so that the tools become available.

  • 1. Unified Geometry Environment
  • 2. Spherical Geometry Environment
  • 3. Unified Geometry Environment B

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3. Introducing Multiple Geometries

We introduce models for several geometries including several finite geometries and the four main infinite geometries that we study as part of Unified Geometry: Euclidean, Hyperbolic (half-plane model), Spherical, and Taxicab Geometries. We see how to model basic objects such as points, lines, line segments, rays, angles, and planes. We use custom tools for the non-Euclidean geometries. We also examine the most basic postulates and properties of incidence.

  • 1. Spherical Geometry Environment
  • 2. Unified Geometry Environment
  • 3. Hyperbolic Geometry: The Poincare Disk Model

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4. Distance and Order

We focus on properties of distance and order in multiple geometries. We see the distance metric in Euclidean, Hyperbolic, Spherical, and Taxicab Geometries.

  • 1. Naming Points, Segments, Rays, and Lines
  • 2. Naming Geometric Objects
  • 3. Centimeter Ruler: Custom Templates
  • 4. Quiz: Distance in the Coordinate Plane (V1)
  • 5. Euclidean and Taxicab Distance
  • 6. AQR Section 37: Taxicab Distance v. Euclidean Distance
  • 7. Hyperbolic Distance Metric

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5. Angles

We introduce angles and angle measure in multiple geometries.

  • 1. Discovering Ways to Name Angles
  • 2. Naming Angles
  • 3. Measuring Angles Using a Protractor
  • 4. Drawing Angles Using a Protractor
  • 5. Naming Angles According to Their Size
  • 6. Creating Angles on a Grid
  • 7. Identifying Angles Around Us
  • 8. Determining Angle Measures Without Tools
  • 9. Drawing Angles: Hot and Cold Activity
  • 10. Drawing Angles Game
  • 11. Creating Angles on a Grid
  • 12. Congruent Angles: Definition
  • 13. Vertical Angles Exploration (2)
  • 14. Vertical Angles Theorem
  • 15. Vertical Angles
  • 16. Adjacent Angles
  • 17. Finding the Missing Angle
  • 18. Complementary and Supplementary Angles
  • 19. Unknown Complementary Angles
  • 20. Supplementary Angles (Quick Exploration)
  • 21. Drawing Parallel, Perpendicular, and Intersecting Lines

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6.A. Triangles in Euclidean Geometry

We explore properties of Triangles in Euclidean Geometry, including classification of triangles, the sum of the measures of the interior angles, and congruence criteria.

  • 1. Euclidean General Triangle measured
  • 2. Classifying Triangles in Euclidean Geometry
  • 3. Exploring Types of Triangles
  • 4. Drawing Triangles
  • 5. Isosceles Triangles in Euclidean,. Hyperbolic, and Taxicab
  • 6. Definition of Congruent Triangles
  • 7. Triangle Congruence
  • 8. SAS Triangle Congruence Exploration Euclidean Geometry
  • 9. SAS: Dynamic Proof!
  • 10. ASA Triangle Congruence Exploration Euclidean Geometry
  • 11. ASA Triangle Congruence Theorem Proof
  • 12. ASA Theorem?
  • 13. SSS Triangle Congruence Exploration Euclidean Geometry
  • 14. SSS: Dynamic Proof!
  • 15. Drawing Triangles
  • 16. Visualizing Triangles
  • 17. Compass and Straightedge Constructions
  • 18. Exterior Angle Inequality Proof with Euclidean Illustration
  • 19. Triangle Exterior Angle
  • 20. AAS Triangle Congruence Exploration Euclidean Geometry
  • 21. Angle-Angle-Side (AAS): Quick Exploration
  • 22. SSA Triangle Congruence Exploration Euclidean Geometry
  • 23. SSA Theorem?
  • 24. AAA Triangle Exploration Euclidean Geometry
  • 25. Sum of Interior Angles of a Triangle
  • 26. Triangle Angle Theorems
  • 27. Triangle Solver
  • 28. Open Middle: Triangle Angles
  • 29. Shortest Distance Theorem
  • 30. Triangle Centers (Euclidean and Hyperbolic Geometry)
  • 31. Triangle Fact (I)
  • 32. 9 Point Circle Action
  • 33. Pythagorean Animation
  • 34. Pythagorean Theorem Animation
  • 35. Finding the Distance Between Two Points Using the Pythagorean Theorem
  • 36. Identifying Right Triangles Using the Pythagorean Theorem

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6b. Triangles in Hyperbolic Geometry

These activities are exploring properties of triangles in the Half-plane model of Hyperbolic Geometry. Among other things, they explore the sum of the interior angles of triangles, and congruence criteria.

  • 1. Hyperbolic General Tiangle Measured
  • 2. SAS Exploration Hyperbolic Geometry
  • 3. ASA Exploration Hyperbolic Geometry
  • 4. Exterior Angle Inequality Proof Hyperbolic Geometry
  • 5. AAS Exploration Hyperbolic Geometry
  • 6. SSS Investigation Hyperbolic Geometry
  • 7. SSA Exploration Hyperbolic Geometry
  • 8. AAA Exploration Hyperbolic Geometry
  • 9. Triangle Centers (Euclidean and Hyperbolic Geometry)

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6.C. Triangles in Spherical Geometry

We explore triangles in Spherical Geometry, including the sum of the measures of the interior angles, and congruence criteria.

  • 1. General Triangle in Spherical Geometry
  • 2. Isosceles Triangle in Spherical Geometry
  • 3. SAS Exploration Spherical Geometry
  • 4. ASA Exploration Spherical Geometry
  • 5. Exterior Angle Inequality Spherical Geometry
  • 6. AAS Exploration Spherical Geometry
  • 7. AAS, AASS Counterexample in Spherical Geometry
  • 8. SSS Exploration Spherical Geometry
  • 9. SSA Exploration Spherical Geometry
  • 10. AAA Exploration Spherical Geometry

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6.D. Triangles in Taxicab Geometry

We explore triangles in Taxicab Geometry, including the sum of the measures of the interior angles, and congruence criteria.

  • 1. Taxicab General Triangle
  • 2. Euclidean Rotation in Taxicab Geometry
  • 3. SAS Exploration Taxicab Geometry
  • 4. ASA and AAS Exploration Taxicab Geometry
  • 5. SSS Exploration Taxicab Geometry
  • 6. SSA Exploration Taxicab Geometry
  • 7. AA(A) Exploration Taxicab Geometry
  • 8. Taxicab Congruent Triangle Counterexamples

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7. Parallel Lines

We introduce properties of parallel lines in multiple geometries. In particular, the Transversal to Parallel Lines Theorem is examined.

  • 1. Transversal to Parallel Lines
  • 2. Transversal Intersects Parallel Lines
  • 3. Alternate Interior Angles Theorem (V1)
  • 4. Same Side Interior Angles Theorem
  • 5. Exploring Alternate Exterior Angles (V2)
  • 6. Exploring Same Side Exterior Angles
  • 7. Vertical Angles Formed by Parallel Lines and a Transversal
  • 8. Alternate Angles Formed by Parallel Lines and a Transversal
  • 9. Corresponding Angles Formed By Parallel Lines and a Transversal
  • 10. Supplementary Angles Formed by Parallel Lines and a Transversal
  • 11. Parallel Lines & Related Angles
  • 12. Identifying Parallel Lines Cut by a Transversal

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8. Quadrilaterals

We examine quadrilaterals in multiple geometries. We explore a robust hierarchical classification scheme for quadrilateral. We then thoroughly explore the properties of each class of quadrilaterals. We also examine congruence criteria for quadrilaterals.

  • 1. Classification of Quadrilaterals in Euclidean Geometry
  • 2. Quadrilateral Angle Theorems
  • 3. Convex quadrilaterals
  • 4. Classifying Quadrilaterals
  • 5. Drawing Quadrilaterals Using Properties
  • 6. Quadrilaterals
  • 7. Mystery Quadrilaterals
  • 8. Quadrilateral Angle Theorems
  • 9. Convex vs. Concave
  • 10. Quadrilateral Creation Templates
  • 11. Kite Action!
  • 12. Kite Template with Investigation Questions
  • 13. Kite in Hyperbolic Geometry
  • 14. Kites in Spherical Geometry
  • 15. Kites in Taxicab Geometry
  • 16. Parallelogram: Theorem 2
  • 17. Parallelogram: Theorem (3)
  • 18. Parallelograms (I)
  • 19. Trapezoid Median (Midsegment) Action!
  • 20. Trapezoid Median: 2 Discoveries
  • 21. Isosceles Trapezoid Template (Scaffolded Discovery)
  • 22. Isosceles Trapezoid Action!
  • 23. Concave Quadrilateral Craziness! (GoGeometry Action 80)
  • 24. Concave Quadrilateral Craziness! (GoGeometry Action 80)
  • 25. Rhombus Action!
  • 26. Quadrilateral Surprise!
  • 27. Quad Midpoints Action!
  • 28. Isosceles Trapezoid Midpoints
  • 29. Compass and Straightedge Constructions
  • 30. Cyclic Quadrilateral: Proof Hint
  • 31. Cyclic Quadrilaterals (IAT: Corollary 3)
  • 32. Quadrilateral "Guess Who?"
  • 33. Square + Rhombus = Constant Surprise! (GoGeometry Action 71)
  • 34. Rotational Symmetry of Quadrilaterals
  • 35. Japanese Theorem for Cyclic Quadrilaterals
  • 36. Quadrilateral Creation Templates
  • 37. Quadrilateral: Exterior Angles
  • 38. Quadrilateral Surprise!
  • 39. Cyclic Quadrilaterals (IAT: Corollary 3)
  • 40. MIdline Quadrilateral 1

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9. Polygons

We examine properties of polygons, particularly those with more than 4 sides.

  • 1. Naming Polygons
  • 2. Parts of a Polygon
  • 3. Sum of Interior Angles of a Polygon
  • 4. Finding the Missing Angle of a Polygon
  • 5. Polygons: Exterior Angles - REVAMPED
  • 6. Property of cyclic polygon
  • 7. Pentagon Angle Theorems

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10. Similarity

The concept of similarity in Euclidean Geometry is examined. Theorems related to similarity are explored.

  • 1. SAS Triangle Similarity Theorem
  • 2. SSS Triangle Similarity Theorem
  • 3. Similar Triangles or Not
  • 4. Parallel Lines Proportionality Theorem
  • 5. Similar Right Triangles (V2)
  • 6. Triangle Midsegment Action!
  • 7. Making Similar Triangles
  • 8. Harmonic Mean In an Isosceles Trapezoid
  • 9. Identifying and Measuring Corresponding Sides of Similar Figures
  • 10. Changing Scale Factor
  • 11. Calculating Scale Factors of Similar Figures
  • 12. Corresponding Parts of Similar Figures
  • 13. Two Transversals to Multiple Parallel Lines
  • 14. Triangle Midlines, Medians, and Centroid
  • 15. MIdline Quadrilateral 1
  • 16. 2 Noncongruent Triangles with 5 Congruent Parts

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14.

11. Circle Theorems

We examine several theorems related to circles in Euclidean Geometry.

  • 1. Circle with Related Figures
  • 2. Circumference = ? (Animation)
  • 3. Equidistant Chord Action
  • 4. Equidistant Chords, Tangent Lines
  • 5. Where to Sit? (I)
  • 6. Inscribed Angle
  • 7. Inscribed Angles Investigation (Revamped)
  • 8. Inscribed Angle Theorem (V1)
  • 9. Inscribed Angle Theorem: Corollary 1
  • 10. Angle Formed by 2 Chords (I)
  • 11. Crossing Chords: Proof Hint
  • 12. Intersecting Secant Lines to a Circle
  • 13. Angle From 2 Secants (V2)

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15.

12. Perimeter, Area

We examine measurement concepts in Euclidean Geometry including length, perimeter, and area. We examine area formulas for several types of geometric figures.

  • 1. Areas of Parallelograms and Triangles
  • 2. Parallelogram: Area
  • 3. Area of a Triangle (Discovery)
  • 4. Triangle Area Action!!! (V2)
  • 5. Triangle Area Action! (V1)
  • 6. Area of a Kite
  • 7. Area of a Rhombus
  • 8. Area of a Trapezoid (Discovery)
  • 9. Area of a Trapezoid
  • 10. Trapezoid: Area (I)
  • 11. Trapezoid: Area (2)
  • 12. Area of a Trapezoid (3)
  • 13. Trapezoid Median: 2 Discoveries
  • 14. Obvious Trapezoid Theorem?
  • 15. Circle Area (By Peeling!)
  • 16. Proof Without Words
  • 17. Pythagorean Theorem Animation
  • 18. Pythagorean Animation
  • 19. Euclid's Proof of the Pythagorean Theorem
  • 20. Geometric Mean Illustration
  • 21. Circle Area (by Peeling)
  • 22. Area of a Circle: Revamped!
  • 23. Visualizing the Area of a Circle and its Formula
  • 24. Pyramids in Prism

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13 Miscellaneous

  • 1. Finding the Treasure on the Coordinate Plane
  • 2. GeoGebra Pentominoes
  • 3. Hangman hexomino cube nets
  • 4. Napoleon Tiling
  • 5. Rhombitrihexagonal Tiling

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14. Volume, 3D Geometry

We examine three-dimensional Euclidean Geometry including classification of 3D figures, surface area, volume, nets, and architectural mats.

  • 1. Volume: Intuitive introduction volume of a cuboid
  • 2. Folding and Unfolding a Net
  • 3. Cube/Prism Net by List of Rotations over the edges
  • 4. Tetrahedron: Exploration Template
  • 5. Net of Polygonal Pyramid
  • 6. Volume of pyramid is 1/3 volume of cube (Method II )
  • 7. Voluem of Pyramid ( Method I )
  • 8. Volume of a Pyramid Using Prism
  • 9. Devide a cube into pyramids
  • 10. Cavalieri's Principle
  • 11. Net of an Octahedron
  • 12. Net of a Dodecahedron
  • 13. Icosahedron Net study
  • 14. Net of a Cone
  • 15. Rhombicuboctahedron's net
  • 16. Images. Polyhedrons and their truncated, critical truncated polyhedra
  • 17. Nets of Right Prisms
  • 18. Unfolding Shapes in 3D
  • 19. Square Pyramid: Underlying Anatomy
  • 20. Cone Anatomy
  • 21. Rectangular Prism: Basic Net Demo
  • 22. Build Your Own Right Triangular Prism (V2)!
  • 23. Making Cross Sections of a Prism
  • 24. Making Cross Sections of a Pyramid
  • 25. Making Cross Sections of a Sphere
  • 26. Making Cross Sections of a Cone
  • 27. Making Cross Sections of a Cylinder
  • 28. cilinderprojectie Gall

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15. Transformations

We examine transformations in Euclidean Geometry including reflections, rotations, translations, glide-reflections, and dilations.

  • 1. Translating Figures
  • 2. Angle Measures of Translated Figures
  • 3. Translating Points to Translate Figures
  • 4. Transformations: Exercise 1
  • 5. Reflecting a Polygon Across Axes
  • 6. Drawing Symmetrical Polygons
  • 7. Creating Your Own Robe Design with Symmetry
  • 8. Visualizing Lines of Symmetry
  • 9. Symmetric Patterns in Nature
  • 10. Rotations: Introduction
  • 11. Rotating Points Around the Origin
  • 12. Mapping a Triangle to a Congruent Triangle Using Reflections
  • 13. Identifying Congruent Figures Using Transformations
  • 14. Exploring a Sequence of Transformations Level 3
  • 15. Transformations Practice 2 (Level 1)
  • 16. Transformations Practice 2 (Level 2)
  • 17. Transformations Practice 2 (Level 3)
  • 18. Transformations Challenge
  • 19. Identifying the Type of Isometry
  • 20. Properties of Dilations
  • 21. Transformation matrices
  • 22. Möbius transformation
  • 23. Möbius transformation
  • 24. Transforming Points on the Coordinate Plane
  • 25. Writing Algebraic Rules for Transformations
  • 26. Proving Triangles Similar (3)
  • 27. AA Similarity Theorem

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Information