Outline
Geometry Collected Resources
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
- Naming Angles According to Their Size
- Measuring Angles
- What is a Radian?
- Identifying Angles Around Us
- Guess the Radian Measure
- Drawing Angles Game Using Radians
- Determining Angle Measures Without Tools
- Drawing Angles: Hot and Cold Activity
- Measuring Angles Using a Protractor
- Drawing Angles Using a Protractor
- Converting Degrees to Radians
- Drawing Angles Game
- Drawing Angles: Hot and Cold Activity
- Creating Angles on a Grid
- Degrees to Radians and Back
- Congruent Angles: Definition
- Vertical Angles Exploration (2)
- Vertical Angles Theorem
- Vertical Angles
- Adjacent Angles
- Finding the Missing Angle
- Estimating Angle Measures Using Radians
- Determining Angle Measures Without Tools
- Complementary and Supplementary Angles
- Unknown Complementary Angles
- Supplementary Angles (Quick Exploration)
- Drawing Parallel, Perpendicular, and Intersecting Lines
- Adding Adjacent Angles
6.A. Triangles in Euclidean Geometry
- Euclidean General Triangle measured
- Classifying Triangles in Euclidean Geometry
- Exploring Types of Triangles
- Relational Parts of a Triangle
- 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
- Pythagorean Animation
- Pythagorean Theorem Animation
- Finding the Distance Between Two Points Using the Pythagorean Theorem
- Identifying Right Triangles Using the Pythagorean Theorem
- Sum of Interior Angles of a Triangle
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
- AAA Triangle Exploration Euclidean Geometry
- 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
- Similar triangles with missing lengths
- Building Similar Triangles
- Building Similar Triangles V2
- Similar Triangles Investigations
- Similar Triangles
- Two Transversals to Multiple Parallel Lines
- Pythagorean and similar triangles.
- 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
- Theorem of Thales
- Intersecting Secant Lines to a Circle
- Angle Formed by 2 Chords (I)
- Angle From 2 Secants (V2)
- Crossing Chords: Proof Hint
12.A. Perimeter, Area
- Areas of Parallelograms and Triangles
- Parallelogram: Area
- Area of a Triangle (Discovery)
- Triangle Area Action!!! (V2)
- Area of a Kite
- Area of a Rhombus
- Area of a Trapezoid
- Area of a Trapezoid (Discovery)
- Trapezoid: Area (I)
- Trapezoid: Area (2)
- Area of a Trapezoid (3)
- Trapezoid Median: 2 Discoveries
- Obvious Trapezoid Theorem?
- Circle Area (By Peeling!)
- Geometric Mean Illustration
- Circle Area (by Peeling)
- Area of a Circle: Revamped!
- Visualizing the Area of a Circle and its Formula
- Finding the Area of Similar Figures Using Scale Factor
- Perimeter of a Rectangle
- Building a Fence and Calculating the Perimeter
- Calculating Perimeter of Polygons
- Calculating the Circumference of a Circle
- Area Fun Using a Grid
- Calculating Areas of Rectangles
- Partitioning Areas of Rectangles with Mixed Number Side Lengths
- Calculating Actual Area Using a Scaled Drawing
- Calculating Area of Composite Figures Using a Quilt Pattern
- Finding the Radius of a Circle
- Visualizing the Area of a Circle and its Formula
12.B. Pythagorean Theorem
- Pythagorean Theorem
- Pythagorean and similar triangles.
- Pythagorean Animation
- Proof Without Words
- Proof Without Words
- Pythagorean Theorem Animation
- Euclid's Proof of the Pythagorean Theorem
- Pythagorean Theorem
- Pythagorean Theorem - a "proof without words"
- Proof of Pythagorean theorem
- Pythagorean Theorem
- Pythagorean Theorem with Technology
- Organic Pythagorean Theorem With Similar Polygons
- The Pythagorean Theorem for a Spherical Right Triangle
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
- Finding the Volume of Similar Figures Using Scale Factor
- Unfolding Shapes in 3D
- Unfolding Prisms
- Unfolding Cylinders
- Unfolding Cones
- Discovering the Formula for the Volume of a Sphere
- Using the Formula for the Volume of a Sphere
- Calculating the Volume of a Sphere
- Composing Prisms by Stacking Cubes
- Calculating Volume with Invisible Cubes
- Calculating the Volume of Composite Solids
- Volumes of Rectangular Prisms
- Volumes of Cylinders
- Connecting Volumes of Pyramids and Prisms Using Visual Models
- Connecting Volumes of Cones and Cylinders Using Visual Models
- Cylinder Volume Word Problems
- 3D Pythagorean Theorem
- Pyramids in Prism
- Cross Sections of a Cube
15.A. Translations
- Translating Figures
- Angle Measures of Translated Figures
- Translating Points to Translate Figures
- Transformations: Exercise 1
- Translating Figures
- Angle Measures of Translated Figures
- Translating Points to Translate Figures
- Describing Horizontal and Vertical Translations of Figures
- Translating Points on a Coordinate Plane
- Translating Points on a Coordinate Plane
15. B. Reflections
15.C. Rotations
15.D. Compositions and Glide-Reflections
15.E. Dilations
15.F. More Transformations
- Mapping a Triangle to a Congruent Triangle Using Reflections
- Transforming Points on the Coordinate Plane
- Identifying Congruent Figures Using Transformations
- Transformations Practice 2 (Level 1)
- Transformations Practice 2 (Level 2)
- Transformations Practice 2 (Level 3)
- Transformations Challenge
- Identifying the Type of Isometry
- Describing Transformations Given an Algebraic Rule
- Writing Algebraic Rules for Transformations
- Identifying Rigid Transformations
- Transformation matrices
- Möbius transformation
- Möbius transformation