Visually Introducing & Classifying a Rhombus
In this activity, you will be visually introduced to a rhombus, and by dragging, visually explore its special cases in relation to other quadrilaterals, and eventually classify them in the form of a 'family tree'. Follow the instructions in the sketch and click on the 'Link to ...' buttons to navigate to the next page.
Visually Introducing & Classifying a Rhombus
Notes
1) This is a suggested, introductory activity on Level 1 (Visualization) of the Van Hiele theory of learning geometry. Since definitions according to the Van Hiele theory only start to become meaningful to students at Level 3 (Informal Deduction), it is also very important to note that the concept of 'rhombus' is also here introduced without any formal definition; only by name and a dynamic visual representation. For more details about the rationale for this approach, read: Note to Teachers, Parents & Mathematics Education Researchers: Investigating Quadrilaterals.
2) The intention of the suggested dynamic activities above is not to replace traditional geometric manipulatives such as cardboard, paper, geoboard or plastic representations of various quadrilaterals, but rather to supplement and compliment those hands-on concrete activities.
3) For an activity for a rhombus on the next Van Hiele level of learning (Level 2), go to: Rhombus: Analysis of properties.
Back to "Introducing, Classifying, Exploring, Constructing & Defining Quadrilaterals"
Back to "Visually Introducing & Classifying Quadrilaterals by Dragging"
Related Links
Rhombus: Analysis of properties
Visually Introducing & Classifying Quadrilaterals
Introducing, Classifying, Exploring, Constructing & Defining Quadrilaterals
Exploring Rhombus Properties (Suggested Grades 4 - 9)
Systematizing Rhombus Properties - Defining a Rhombus (Suggested Grades 8 - 10)
Note to Teachers, Parents & Mathematics Education Researchers: Investigating Quadrilaterals
Some Van Hiele theory video clips and invited papers
A Hierarchical Classification of Quadrilaterals
Definitions and some Properties of Quadrilaterals
Semi-regular Angle-gons and Side-gons (Generalizations of rectangles and rhombi)
Golden Rhombus: an Example of Constructive Defining
A diagonal property of a Rhombus constructed from a Rectangle
A Rhombus Angle Trisection Result
A generalization of Paul Yiu's problem
The 120o Rhombus (or Conjoined Twin Equilateral Triangles) Theorem
Opposite Side Quadrilateral Properties by Kalogerakis
Van Aubel's Theorem and some Generalizations
***************
Free Download of Geometer's Sketchpad
***************
Back to "Dynamic Geometry Sketches"
Back to "Student Explorations"
Created by Michael de Villiers in July 2008; converted to WebSketchpad, 31 Oct 2025.