Halving a Triangle Perimeter

semiperimeter rotation fraction

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The perimeter of a triangle is the sum of its sides. This Demonstration draws a gray line that halves the perimeter of the triangle. If and only if that line halves the area, then it goes through the incenter point

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in red. If the line goes through a green midpoint, then it is called a cleaver and goes through the Spieker center

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in green. If the line goes through a vertex, then it is called a splitter and goes through the Nagel point

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in blue. As you move the gray line around, the midpoint in magenta traces the outline of a a smaller triangle.