## Segment Addition Postulate: Hanging Pictures

September 14, 2018

I just did an activity with my Pre-AP Geometry classes that I am fairly proud of. It occurred to me this summer, when I was hanging a bunch of pictures, that I was actually doing a practical application of the Segment Addition Postulate.

Origin Story
It all started when I was hanging my Captain America picture display.

I decided I wanted the five pictures centered on the wall and centered vertically on each other. I thought the math involved in making that happen was interesting, so I came up with a slightly simpler version (DOC) (PDF) for my students.

The Setup
When I introduced the problem, I brought one of the pictures from home to show them what I was working with. I realized that my back blackboard was 12′ long, the same width as my wall, so I decided to make full-size “pictures” for them to arrange once they had their measurements.

What I Learned
I have two Pre-AP Geometry classes on alternate days. The first day, I introduced the problem and just told them to get started. This led to quite a bit of confusion, and I had to spend some time answering the same questions over and over. I thought it was fascinating that two approaches emerged — some groups were making their calculations using the information I gave them, which was pretty much the way I intended them to go. Another group, however, decided they were frustrated with the numeric approach and went directly to the full-size shapes to arrange first. They finally got everything arranged, but the whole “display” was too far to the left, so they had to shift everything over. Once they had, they went back and measured where everything was “supposed” to go. Their numbers weren’t exactly the same as mine, but I was pleased by how close they were.

On the second day (especially since my principal and evaluator were coming), I decided to give them a little more direction before turning them loose. We went through the process of finding the center of the display and how to line that up with the center of the room. I also explained how to align the pictures vertically with each other so that the tallest was 14″ from the ceiling. Overall, it went much more smoothly, and I had fewer students get frustrated and just quit.

Both my principal and evaluator complimented me on the lesson design, and on the “real-world” aspect of the problem. Admittedly, I’m not sure too many people would be as anal as I am about getting pictures aligned in this fashion, but I think the principles can be applied to a lot of practical situations.