My colleague Scott Steketee recently shared a problem with me that makes for a nice Web Sketchpad exploration: Construct two segments, AB and CD, that bisect each other. Connect points A, B, C, and D to form a quadrilateral. What kinds of quadrilaterals can you make by dragging the vertices?

Using the websketch below (and here), you can construct two segments that bisect each other and form the quadrilateral (see this accompanying video for all the details.)

Quadrilateral ABCD is always a parallelogram. It’s possible to drag the vertices so that ABCD approximate a rhombus, a rectangle, or a square. But can we add to the construction without starting over so that ABCD is always a rhombus, always a rectangle, or always a square? The answer is yes, using Web Sketchpad’s unique “drag merge” feature. The video referenced above shows how to do so.