The Interior Angles of a Triangle Sum to Pi

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The interior angles of any plane triangle can together form a straight line. This is illustrated by the blue triangle, which has one vertex fixed at the origin and its two other vertices shaded in yellow and green. The two gray auxiliary triangles are congruent to the blue triangle, and are positioned to form a straight line through the origin. Use the slider to clarify the relationships between the various angles.

Contributed by: John Custy (November 2011)
Open content licensed under CC BY-NC-SA


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