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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
Drawing vs. Constructing, The Drag Test
2. Basic Unified Geometry Environments
Unified Geometry Environment
Spherical Geometry Environment
Unified Geometry Environment B
3. Introducing Multiple Geometries
Spherical Geometry Environment
Unified Geometry Environment
Hyperbolic Geometry: The Poincare Disk Model
4. Distance and Order
Basic Objects
Naming Points, Segments, Rays, and Lines
Naming Geometric Objects
Centimeter Ruler: Custom Templates
Quiz: Distance in the Coordinate Plane (V1)
Euclidean and Taxicab Distance
AQR Section 37: Taxicab Distance v. Euclidean Distance
Hyperbolic Distance Metric
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
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.
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.
We focus on properties of distance and order in multiple geometries. We see the distance metric in Euclidean, Hyperbolic, Spherical, and Taxicab Geometries.
1. Basic Objects
2. Naming Points, Segments, Rays, and Lines
3. Naming Geometric Objects
4. Centimeter Ruler: Custom Templates
5. Quiz: Distance in the Coordinate Plane (V1)
6. Euclidean and Taxicab Distance
7. AQR Section 37: Taxicab Distance v. Euclidean Distance
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. Relational Parts of a Triangle
5. Drawing Triangles
6. Isosceles Triangles in Euclidean,. Hyperbolic, and Taxicab
7. Definition of Congruent Triangles
8. Triangle Congruence
9. SAS Triangle Congruence Exploration Euclidean 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.
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
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
25. Finding the Area of Similar Figures Using Scale Factor
26. Perimeter of a Rectangle
27. Building a Fence and Calculating the Perimeter
28. Calculating Perimeter of Polygons
29. Calculating the Circumference of a Circle
30. Area Fun Using a Grid
31. Calculating Areas of Rectangles
32. Partitioning Areas of Rectangles with Mixed Number Side Lengths
33. Calculating Actual Area Using a Scaled Drawing
34. Calculating Area of Composite Figures Using a Quilt Pattern
35. Finding the Radius of a Circle
36. Visualizing the Area of a Circle and its Formula