## Classifying Quadrilaterals Visually by Dragging

by Michael de Villiers

In this activity, you will visually explore the relationship between several different quadrilaterals and eventually classify them in the form of a 'family tree'. After a visual introduction to a square and a rectangle, 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, bisecting quadrilateral, cyclic quadrilateral and eventually a circum quadrilateral.

Note for Teachers or Parents

#### .sketch_canvas { border: medium solid lightgray; display: inline-block; }

Now continue with the JavaSketchpad activities below (that have not yet been converted to the newer WebSketchpad). Also note that you'll need to have the latest Java enabled on your browser, and some pages may need to be refreshed to work properly.

Activity 5: Isosceles Trapezoid (trapezium)

Activity 6: Kite

Activity 7: Trapezoid (trapezium)

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.

My book Some Adventures in Euclidean Geometry 219 pp. @ USD 4.00 to download - printed copy also available @ USD 19.99 or iTunes version @ \$9.99 for iPhone, iPad, or iPod touch - gives extensive attention to the defining and classification of the quadrilaterals from the symmetry of a side-angle duality. My book Rethinking Proof with Sketchpad also contains some dynamic classifying activities for an Isosceles Trapezoid and a Circumscribed Quadrilateral, and some discussion in the Teacher Notes. An excellent book is Shape Makers with Sketchpad by Michael Battista, which a follows a similar, though different approach to that below, and in Southern Africa is available for ordering from Dynamic Mathematics Learning.

Created, 2008; most recently modified by Michael de Villiers, 20 September 2016.