Exploring the Properties of (some) Quadrilaterals

by Michael de Villiers

In this activity, you will explore the properties of the following five quadrilaterals in terms of their angles, sides, diagonals, symmetry, etc.: rectangle, rhombus, parallelogram, isosceles trapezium and kite. You are encouraged to investigate the properties by dragging and checking that a particular quadrilateral passes the 'drag test' in regard to a particular property; in other words, that it always has that property no matter how much you drag it. An important part of mathematics is formulating your conjectures and logically explaining them. An opportunity to check your formulations and explanations is given in two quizzes in each activity.

Important: Before starting this investigation, ensure that you have already completed the previous Investigation 1: Classifying quadrilaterals visually by dragging for at least the five quadrilaterals concerned in this investigation, and established a hierarchical classification for them. Note that in such a hierarchical classification the special cases lower down inherit all the properties of the more general cases above them. An extended, interactive classification of many different quadrilaterals is also available at Hierarchical Quadrilateral Tree.

Click on the picture icons to the left of the names of the quadrilaterals below to open the Property Exploration for each of the five quadrilaterals below.
(Note that so far only the Kite and Rhombus activities below have been converted to WebSketchpad)

Kite	Parallelogram	Isosceles trapezium
Rhombus		Rectangle

Compartive Summary of Properties
Print out, or copy a table of the following properties, and tick of which quadrilaterals have which properties.
Summary of various Quadrilateral Properties

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Created by Michael de Villiers, 4 October 2011 with JavaSketchpad; converted to WebSketchpad, 20 July 2025; updated 16 Nov 2025.