# Why It Works: Exterior Angle Theorem

Why It Works

Motion graphics were created by Mac Square.

How do you make sense of the Exterior Angle Theorem? What activities or resources have you used with your students to investigate the why?

Makes sense when you draw equilateral. Extend exterior. It’s 120 because supplementary [angles]. What do you notice about sum of remote interior angles furthest from exterior? It’s equal. Then I thought of right triangles. You know the exterior angle is 90. The 2 remote interior must also add up to 90 because they’re complementary to each other.

I like this sequence as a “spot pattern, make conjecture” intro. Follow up with “proof” by exhaustion: each student cuts out a triangle, tear off interior angles and lay on exterior to show equal; but still not proven for all triangles. So technology can help us check more triangles quickly: geogebra.org/m/babbmfWc. Ah but how did Euclid knew true? Formal proof following insight from GeoGebra: opposite angles, corresponding angles congruent.