Why do these paths all have the same length?

By a sequence of reflections of setions of each path ... each path can be shown to the same length as the red path.

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Turn the picture by about $55^\circ$ clockwise, so that the paths are made of horizontal and vertical segments.

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Then you will see that any of those paths is as long as it takes to move from $A$ to the 'right', all the way to the place 'right above $B$' and then move 'down' all the way to $B$ (darker black line added on the picture).


When I was 5th grade student or something like that, I couldn't understand how they could be equal in a similar question and one of my brothers showed me a figure as I drawed and I completely understand it when I saw that figure. The figure I attached is as same as that one and since I didn't want to mess up the original one, I showed it on path $I$ and $II$:

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Note that same colored segments have the same length.

Tags:

Geometry

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