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 activity has been updated to WebSketchpad)
Investigation 3: Constructing Quadrilaterals (Grades 7-10) (Needs to be updated to WebSketchpad)
Investigation 4: Defining Quadrilaterals (Grades 9-10) (under construction)
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Related Links
A Hierarchical Classification of Quadrilaterals
Definitions and some Properties of Quadrilaterals
Some Van Hiele theory video clips and invited papers
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
Similar Parallelograms: A Generalization of a Golden Rectangle propertys
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 Centroid (centre of gravity or balancing point) 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
Finsler-Hadwiger Theorem plus Gamow-Bottema's Invariant Point
Generalizations of a theorem of Sylvester
Van Aubel's Theorem and some Generalizations
Rethinking Proof Activities
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Free Download of Geometer's Sketchpad
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Back to "Student Explorations"
Back to "Dynamic Geometry Sketches"
Creatd by Michael de Villiers in 2011, modified 31 May 2013; updated 28 Feb/13 March 2025; 20 July 2025.