The Varied Paths to Constructing a Rhombus

In how many different ways can you build a rhombus that stays a rhombus when its vertices are dragged? This assignment, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the quadrilateral.

While the rhombus task works well, it does expose some challenges of using Sketchpad: The software features lots of menu commands and toolbox options, and navigating all this functionality can sometimes distract Sketchpad newcomers from the mathematics at hand.

Web Sketchpad differs from Sketchpad by offering  a more streamlined approach to mathematical construction. It allows a teacher or curriculum developer to create and provide only those tools needed for a particular task. In this manner, we can lead students to think about a problem in targeted ways by limiting them to carefully chosen tools. To support this goal, we’ve just added a new feature to Web Sketchpad that allows a multi-page websketch to contain different tools on each page.

Below (and here) is a seven-page websketch. To navigate between the pages, use the arrows in the lower-right corner of the websketch. On each page, you’ll find a unique set of tools that focus on different mathematical properties of a rhombus. Your task is to construct a rhombus with each toolset so that your quadrilateral stays a rhombus when its vertices are dragged.

Give it a try—are some of your rhombi more general or robust than others? Are some overconstrained? Do some construction methods seem more elegant? What geometric properties of a rhombus does each construction exploit?

If you need help, watch the movie at the end of this post that demonstrates the rhombus constructions. If you’d like to create your own construction challenges, check out the Web Sketchpad Tool Library and Viewer, where you have access to over 60 tools that you can mix and match together.

 

 

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