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How do we know the triangles are equilateral?

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By: Tim Lehman

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Because the hexagon is regular, we know that all of the central angles are equal. Thus, they can be found by dividing 360 degrees by 6. Each central angle is then 60 degrees. All the base angles of the triangles are equal (Note: opposite sides of hexagon are equal.) Thus, they can be found by subtracting 60 degrees from 180 (the sum of all the angles of the triangle) and dividing by 2 (because they are all equal). The angles are 60 degrees as well. Therefore, the triangles are equilateral.