Classifying Quadrilaterals Visually by Dragging

by Michael de Villiers

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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 an introduction to a square and a rectangle, you will 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

My book Some Adventures in Euclidean Geometry 219 pp. @ USD 4.00 to download - printed copy also available @ USD 26.99 gives extensive attention to the defining and classification of the quadrilaterals from the symmetry of a side-angle duality.

An Introduction to a Square and a Rectangle

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Activity 1: Rectangle-Square Relationship

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What does the above investigation tell you about the relationship between a rectangle and a square?

Go to Rectangle-Square-solution


Now continue with the activities below. (Some pages may need to be refreshed to work properly).

Activity 2: Rhombus-Square

Activity 3: Rectangle-Rhombus

Activity 4: Parallelogram

Activity 5: Isosceles Trapezoid

Activity 6: Kite

Activity 7: Trapezoid

Activity 8: Bisecting Quadrilateral

Activity 9: Cyclic Quadrilateral

Activity 10: Circum 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.

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Modified by Michael de Villiers, 3 August 2008 with The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.