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.

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

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

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

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

8. Regular Pentagon
Proof by area of triangles

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