Note for Teachers, Parents or Mathematics Education Researchers
Due to the hierarchical structure of the investigations, with each one building on the preceding ones, it is advisable to do the investigations in the order in which they appear below. Suggested Grades are indicated.
Dynamic Investigations
Investigation 1: Visually Introducing & Classifying Quadrilaterals by Dragging (Grades 1-7)
Investigation 2: Exploring the Properties of (some) Quadrilaterals (Grades 4-9) (Kite, Rhombus & Isosceles Trapezoid activities have been updated to WebSketchpad)
Investigation 3: Constructing Quadrilaterals (Grades 6-10) (Rhombus & Isosceles Trapezoid activities have been updated to WebSketchpad)
Investigation 4: Defining Quadrilaterals (Grades 8-10) (Rhombus & Isosceles Trapezoid activities have been updated to WebSketchpad)
***************
Related Links & some Videos
Rethinking Proof Activities
Invited Nacome Plenary 2021: Does Dynamic Computer Verification imply the End of Proof? (YouTube video)
Some Van Hiele theory video clips and invited papers
A Hierarchical Classification of Quadrilaterals
Definitions and some Properties of Quadrilaterals
Area Formula for Quadrilateral in terms of its Diagonals
Area ratios of some parallel-polygons inscribed in quadrilaterals and triangles
Maximum area of quadrilateral problem
Bretschneider's Quadrilateral Area Formula & Brahmagupta's Formula
Midpoint Trapezium Theorem
Some Trapezoid (Trapezium) Explorations
Midpoint trapezium (trapezoid) theorem generalized
Matric Exam Geometry Problem - 1949
Golden Quadrilaterals: Examples of Constructive Defining
Similar Parallelograms: A Generalization of a Golden Rectangle property
Parallelogram Distances
Feynman Parallelogram Generalization
Area Parallelogram Partition Theorem
Another parallelogram area ratio
Crossed Quadrilateral Properties
Finding the Area of a Crossed Quadrilateral (PDF)
A Rectangle Angle Trisection Result
A Rhombus Angle Trisection Result
A diagonal property of a Rhombus constructed from a Rectangle
Cross's (Vecten's) theorem & generalizations to quadrilaterals
Point Mass (Vertex) Centroid of Quadrilateral
More Properties of a Bisect-diagonal Quadrilateral
Pythagorean & Orthodiagonal Quadrilaterals
Another Property of an Opposite Side Quadrilateral
A Property of an Opposite Angle Quadrilateral
Side Divider Theorem for a Tangential Quadrilateral (A generalization of Conway's circle theorem)
Angle Divider Theorem for a Cyclic Quadrilateral (Dual to the above result)
Finsler-Hadwiger Theorem plus Gamow-Bottema's Invariant Point
Generalizations of a theorem of Sylvester
Van Aubel's Theorem and some Generalizations
External Links
Quadrilateral (Wikipedia)
Aimssec Lesson Activities (African Institute for Mathematical Sciences Schools Enrichment Centre)
UCT Mathematics Competition Training Material
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.)
***************
Free Download of Geometer's Sketchpad & Learning/Instructional Modules on various topics
***************
Back to "Student Explorations"
Back to "Dynamic Geometry Sketches"
Created by Michael de Villiers in 2011, modified 31 May 2013; updated 28 Feb/13 March 2025; 20 July 2025; 3 Nov 2025; 15 Jan 2026; 30 April 2026.