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Routh Triangle Interior Angles

Interact with this app for a few minutes. Then answer the questions that follow. Note: LARGE POINTS are moveable.

Try to get the vertices of the triangle's 3 angles to coincide (lie on top of each other). Move these sectors (circle pieces) around so they don't overlap. Notice anything interesting? If so, describe.

If you added the three angles of a triangle together, what would be the sum?