#MTBoS30: Proving Parallelograms Pong

For the first time, in Geometry I taught a lesson about proving quadrilaterals on the coordinate plane are parallelograms.

We used three methods: slope, distance formula, and a combination of slope and distance formula. We never actually used a coordinate plane. I had students sketch the parallelogram and label the vertices in the order of the given ordered pairs.

I want to point out here that it's important to explain how to label quadrilaterals because for triangles, the order doesn't really matter. Now it does, and mixing up the letters can change a side to a diagonal and really throw them off.

Then I asked them, what two sides should be parallel or congruent to form a true parallelogram? This gave them a starting point to set up there problems and solve.

To practice, I made my go-to Pong powerpoint (see: all the pongs). It's not awesome because the answers are just yes and no and don't have worked out solutions. But considering that I could find nothing else on this topic, it's better than nothing, Literally.

My original thought was a Desmos activity but I couldn't figure anything out. I think seeing the ordered pairs on the coordinate plane would lead students to just guess yes or no based on it's looks and lose all the motivation to actually work the problem out.

Any ideas?


  1. My first thought was having a 5th point M (potential midpoint) and using distance to see if each diagonal was truly bisected. Then I thought just verify the diagonals have the same midpoint. Just check slide 8 first. But I do like it! And I agree about the graph paper, but our eoc allows unlimited graph paper and I always tell my kids to graph anything with coordinates.