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Is the shortest vertical segment a basic fact?
It is indeed a basic fact that the vertical segment is the shortest.

The shortest vertical line segment is the most basic but commonly used largest model. Many complex maximum models will eventually be transformed into the shortest vertical line segment, such as the famous "Hu Bugui" model. The shortest vertical line segment is a basic mathematical fact and a basic principle in geometry. It means that of all the connecting lines from a point to a straight line, the line perpendicular to this straight line is the shortest. This principle can be proved by Pythagorean theorem, and can also be verified by actual measurement and observation.