For Theorem: Two lines that are perpendicular to the same line are parellel to each other. For this theorem, I will ask the students if they ever wondered why cities—as seen from an airplane window—seem “squarish.” All the roads are parallel and perpendicular. The reason they do this is for better navigation and an easier way of getting around. Can you imagine a city that had chaotic roads like this . I’ll finish by sharing a story of how I recently went to New York and got lost, but remembered the streets were parallel and perpendicular and followed a street until I found my hotel.
I also tell them a story of how one time I tried to beat traffic by exiting two exits early to take the side roads. What I didn’t realize was that the exit I took was not parallel to the street I was trying to get to, and I ended up getting lost because of that assumption (I draw a diagram on the board to illustrate).