Exploring Rhombus properties

Exploring Rhombus Properties (Suggested Grades 4 - 9)

Exploring Rhombus Properties (Suggested Grades 4 - 9)
In this activity, you will explore the properties of a rhombus, and by dragging, particularly look at its sides, angles, diagonals, and circle properties. If not already done, it is recommended to first complete the following activity: Visually Introducing & Classifying a Rhombus before continuing with the one below.

Explore
1) Explore the properties of a rhombus below by dragging vertices A, B, or C. (Click on the buttons to display relevant measurements).
Alternatively, click on the 'Link to No measurements' button to navigate to a new sketch, and use the tools given on the left to make these measurements yourself.
2) What do you notice about its sides, angles, diagonals, symmetry? Does it have a circumcircle or incircle?

Conjecturing & Checking
3) Write down your conjectures in relation to your observations in 1).
4) Then check your conjectures by completing this Rhombus Properties Quiz which will open in a new browser window. Continue until you get a % score and you are told you've completed the exercise. If you do not get 100%, repeat your dynamic exploration in 1) above.

Exploring Rhombus Properties

Logically Explaining
5) Explain (prove) using the symmetry of the rhombus why your conjectures in 2) to 4) are true.
6) After writing your explanations down, check and compare them with those in this exercise Rhombus Properties Explanations.

Notes
a) 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, and activities like folding & measuring by hand, but rather to supplement and compliment those hands-on concrete activities.
b) This is a suggested activity on Level 2 (Analysis of properties) of the Van Hiele theory of learning geometry. For an activity for a kite on the previous Van Hiele level of learning (Level 1), go to: Visually Introducing & Classifying a Rhombus.
c) For a transitional activity towards the next Van Hiele level of learning (Level 3: Systematizing/Defining a rhombus), go to: Free construction of a rhombus (not yet converted to WSP).
d) Ideally, in the activity at the top, if time allows, learners & students should measure sides, angles, etc. themselves. To do so yourself, click on the 'Link to No Measurements' button to navigate to a new sketch & use the tools on the left to measure sides, angles, etc.
e) For an activity on the next Van Hiele level of learning (Level 3: Systematizing/Defining a rhombus), go to: Systematizing Rhombus Properties - Defining a Rhombus (Rethinking Proof activity).

Back to "Introducing, Classifying, Exploring, Constructing & Defining Quadrilaterals"

Back to "Visually Introducing & Classifying Quadrilaterals by Dragging"

References
Bennett, Dan. (2012). Properties of Rhombuses, pp. 158-160. Exploring Geometry with Geometer's Sketchpad (free to download). Key Curriculum Press.
De Villiers, M. (1999, 2003, 2012). The van Hiele Theory — Defining and Proving Within a Dynamic Geometry Context. Introductory chapter from Rethinking Proof with Geometer's Sketchpad (free to download). Key Curriculum Press. De Villiers, M. (2011). Simply Symmetric. Learning and Teaching Mathematics, No. 11, pp. 22-26.

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Created by Michael de Villiers, 23 September 2011 with JavaSketchpad; converted to WebSketchpad, 1 Nov 2025.