TITLE: The shortest distance between any two distinct points is the line segment joining them.How can I see why this is true?
QUESTION [18 upvotes]: On a euclidean plane, the shortest distance between any two distinct points is the line segment joining them. How can I see why this is true?

REPLY [4 votes]: Think of all possible paths as geometrical figures. In a  triangle, the sum of any 2 sides is greater than the 3rd side. Hence if you go by any other path other than a straight line, you travel more.