A Bevy of Rhombus Constructions

In my January 2020 blog post, I presented a collection of Web Sketchpad construction challenges where the goal was to use each handpicked set of tools to build a rhombus. Could you, for example, construct a rhombus with just a Compass and Parallel tool? How about starting with merely the Reflect tool?

These kinds of construction challenges have become one of my favorite ways to use Web Sketchpad. Rather than giving students a mountain of tools and letting them decide which to use, we limit the tools, creating construction puzzles where students consider how the properties of the shape they are constructing mesh with the handful of tools provided to them.

This summer, we’re undertaking an exciting partnership for Web Sketchpad that we’ll write about soon. As part of this project, Scott and I revisited our rhombus construction challenges and tweaked them. I considered simply updating the January 2020 post with our changes, but decided that from a curriculum design standpoint, it might be useful to leave the original construction challenges intact as a record of how our thinking evolved.

In the websketch below (and here), use the tools on each of its 11 pages to construct a rhombus. When you’ve built your rhombus, experiment with the “fitness” of your construction: Does your quadrilateral stay a rhombus no matter which points you drag? Does it change size but always maintain the same shape? Or does it change both its size and shape while remaining a rhombus? For some toolsets, it isn’t possible to build a rhombus that has this degree of flexibility.

Notice that there is a quadrilateral ABCD that sits at the bottom of each page. One by one, you can drag and merge the vertices of this quadrilateral to the points that you believe define a rhombus. If you’ve indeed constructed a rhombus, the message will switch from “Not a rhombus” to “Rhombus!”

The YouTube video here demonstrates this “drag merge” feature and offers ideas for constructing a rhombus using the tools on pages 1-7 of the websketch.

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