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.

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

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

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

Regular Pentagon Proof by area of triangles

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