Visualizing a Dynamic Triangle

Below is a problem taken from Dietmar Küchemann’s Algebradabra site.

Many problems that mix geometry with algebra invariably shortchange the geometry. For example, the angles of a triangle might be labeled x, 2x, and 3x, and students are asked to find the value of x. Other than knowing that the angles of a triangle sum to 180°, there is no geometric reasoning required to compute x.

Küchemann’s scenario, however, is different. While there is an x involved, the goal is not to solve for it. Rather, the intent is to visualize and describe the transformation that ∆ABC undergoes as x grows larger.

While this problem is best approached without any technology at all, I couldn’t resist modeling it with Web Sketchpad. This YouTube video shows how to construct the triangle using the websketch below (and here). Page 2 of the websketch displays the completed construction.