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Cincinnati’s Proof

Cincinnati’s Proof. Given an equilateral triangle and any interior point, the perpendicular segments from the point to any sides sum will be constant. First step of proof: divide the original triangle into three smaller triangles using the perpendicular segments as their altitudes.

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Cincinnati’s Proof

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  1. Cincinnati’s Proof Given an equilateral triangle and any interior point, the perpendicular segments from the point to any sides sum will be constant.

  2. First step of proof: divide the original triangle into three smaller triangles using the perpendicular segments as their altitudes.

  3. What about other polygons: Rectangle Rhombus Regular Pentagon Hexagon with only opposite sides parallel

  4. Rectangle - Yes • This is because the distance between parallel lines is constant. Distance is always measured with a perpendicular.

  5. Rhombus • Prove using: • A. Distance between parallels is constant. • B. Area of triangles as an equal length that can be factored.

  6. Regular Pentagon • Proof by area of triangles

  7. Hexagon with only opposite sides parallel • Proof by distance between parallel lines are constant.

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