Teaching Triangle Angle Sum

The Triangle Angle Sum Theorem is one of my favorite topics in Geometry class. It’s a foundational fact about triangles, and in geometry, every problem is a problem about triangles.

I love the standard proof of the theorem, where a line is constructed through a vertex that is parallel to the opposing side. It highlights the crucial role that parallel lines play in our conception of geometry, and it points to the assumptions we make about them as well. With a little nudge, this standard proof is eminently discoverable, and makes for a great classroom activity.

But I also love showing students some non-standard proofs of the theorem. Here’s a demonstration I built in Geogebra meant to mimic a paper folding activity that shows how the angles of a triangle form a straight line.

You should do it with actual paper, too! Here’s a short video. Stick around for the bonus tearing at the end!

Apart from being fun and surprising, what I like about these demonstrations is how they illuminate something important and essential about result: It’s the straight line, not the number 180, that’s important. Plus, the tearing activity works with more than just triangles! Unfortunately it’s not so adaptable to spherical geometry, but that’s another lesson.

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