*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?

Martin Joyce via Twitter:

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.

Andrew Knauft via Twitter:

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.

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