WOLFRAM|DEMONSTRATIONS PROJECT

Halving the Perimeter of a Zigzag Polygon

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altitude
angle
show angle and proof
A a closed zigzag polygon is made from two isosceles triangles with base 1 and altitude
h
, and a similar triangle with base 2. A straight line through the origin
O
and inclined at an angle
ϕ
cuts the polygon into two parts. What is the length of the blue part?