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