There are a few different ways of looking for the center of a triangle. My geometry students did the section in the textbook, then made cutouts on the laser.
They got some practice designing the triangles using a vector graphics program (Corel Draw). This did require an explanation of the difference between vector and raster images, since the majority of the class was unfamiliar with the concept. Raster images are made up of a grid of pixels, while vector images have instructions for where points go and where to draw lines. Vector images are great for diagrams like these because the files can be much smaller, the lines are more precise, and you can scale them up or down without losing any of that precision.
It turned out to be very useful to have them create the shapes and intersecting lines on the computer. It was pretty easy for them to precicely measure angles and find midpoints, so they could find the center points with much more accuracy than they could on just paper.
Having the final triangle cut-outs were also interesting. The centroid–the point of intersection of lines going from the vertices to their opposite side–is the center of gravity of the triangle, which means that, if you’re careful, you can use that point to balance the cut-out triangle on the tip of a pencil.
