Visually Introducing & Classifying Quadrilaterals by Dragging

Visually Introducing & Classifying Quadrilaterals by Dragging (Grades 1-7)

by Michael de Villiers

Back to "Introducing, Classifying, Exploring, Constructing & Defining Quadrilaterals"

Visually Introducing & Classifying Quadrilaterals
In this series of activities, you will be visually introduced to several different quadrilaterals and visually explore the relationship between them, and eventually classify them in the form of a 'family tree'.
After a visual introduction to a square and a rectangle below, you will further explore the relationship between a rectangle and a square. Then you will move on to a rhombus, parallelogram, isosceles trapezoid, kite, trapezoid, bisect-diagonal quadrilateral, cyclic quadrilateral and eventually a circumscribed quadrilateral.
Note: In the dynamic sketch below you can navigate to the next activity by using the 'Link to' buttons in each page. Alternatively, use the separate individual links given to each quadrilateral below the dynamic sketch.

Note for Teachers, Parents or Mathematics Education Researchers

It is assumed below that young learners would be intuitively introduced to the general concept of 'quadrilateral' simply as a closed figure in the plane with four straight sides. The intention of the suggested dynamic activities below is not to replace traditional geometric manipulatives such as cardboard, paper, geoboard or plastic representations of various quadrilaterals, but rather to supplement and compliment those hands-on concrete activities.

Web Sketchpad

Visually Introducing & Classifying Quadrilaterals

Separate Links
The JavaSketchpad activities for an isosceles trapezoid, kite, trapezoid, bisect-diagonal quadrilateral, cyclic quadrilateral and a circumscribed quadrilateral are listed separately below. Unfortunately Java is no longer working, but these activities will be updated to the newer WebSketchpad in due course.

Activity 5: Isosceles Trapezoid (trapezium)

Activity 6: Kite (dart)

Activity 7: Trapezoid (trapezium) (Updated to WebSketchpad)

Activity 8: Bisect-diagonal Quadrilateral

Activity 9: Cyclic Quadrilateral

Activity 10: Circumscribed (tangential) Quadrilateral

Activity 11: Now draw a tree diagram starting with a general convex quadrilateral at the top, showing a combined classification of all the quadrilaterals explored above and the relationships between them.

Self-Evaluation: Complete this self-testing quiz of 10 questions to check your classification in Activity 11, and your understanding of the relationships between the quadrilaterals. If you do not get 100%, or very close to it, you may have some mistakes in your tree diagram (classification) and you should again carefully go through some of the above activities.

Some References & Links
Battista, M.T. (1998). Shape Makers: Developing Geometric Reasoning With the Geometer's Sketchpad - Grades 5-8. Key Curriculum Press. (Free to download - click on link). Click here to download the corresponding zipped Sketchpad sketches.
Battista, M.T. (2001). Shape Makers: A Computer Environment That Engenders Students' Construction of Geometric Ideas and Reasoning. Computers in the Schools, 17(1-2), 105-120. https://doi.org/10.1300/J025v17n01_09
Bennett, D. et al (2012). Exploring Geometry and Measurement with Geometer's Sketchpad - Grades 3-5. Key Curriculum Press. (Free to download - click on link). Click here to download the corresponding zipped Sketchpad sketches.
Bennett, D. et al (2012). Exploring Plane and Solid Geometry - Grades 6-8. Key Curriculum Press. (Free to download - click on link). Click here to download the corresponding zipped Sketchpad sketches.
Bennett, D. & Albrecht, M. (2012). Exploring Geometry with Geometer's Sketchpad - Grades 8-11. Key Curriculum Press. (Free to download - click on link). Click here to download the corresponding zipped Sketchpad sketches.
De Villiers, M. (2009). Some Adventures in Euclidean Geometry. Lulu Publishers. (Free to download - click on link).
De Villiers, M. (2012). Rethinking Proof with Geometer's Sketchpad. Key Curriculum Press. (Free to download - click on link).
Furner, J.M. & Marinas, C. A. (2007). Geometry Sketching Software for Elementary Children: Easy as 1, 2, 3. Eurasia Journal of Mathematics, Science & Technology Education, 3(1), 83-91. (Free to download - click on link).
Human, P.G. & Nel, J. H. et al. (1987). Alternative Instructional Strategies for Geometry Education: A Theoretical and Empirical Study. (Final theoretical part of the report of the University of Stellenbosch Experiment in Mathematics Education (USEME)-project: 1977-78), University of Stellenbosch. (Click on link).
Patsiomitou. S. (2019). A Trajectory for the Teaching and Learning of the Didactics of Mathematics: Linking Visual Active Representation. Global Journals Incorporated, United States. (Free to download - click on link).
Scher, D. & Rasmussen, S. (2009). Teaching Mathematics with Geometer's Sketchpad. Key Curriculum Press. (Free to download - click on link).
Sketchpad Activities for Young Learners - Grades 3-5.
Some Van Hiele theory video clips and invited papers.

Next Investigation
For the next investigation, click on the links below to go:
Back to "Introducing, Classifying, Exploring, Constructing & Defining Quadrilaterals"
Or directly to Investigation 2: Exploring the Properties of (some) Quadrilaterals

External Link
SA Mathematics Olympiad
Questions and worked solutions for past South African Mathematics Olympiad papers can be found at this link.
(Note, however, that prospective users will need to register and log in to be able to view past papers and solutions.)

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Free Download of Geometer's Sketchpad

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Created, 2008 by Michael de Villiers; modified 20 September 2016; updated 28 Feb 2025; 3 March 2025.