What are the Intrinsic properties of Euclidean spaces?

Question

I am reading a book "An introduction to Manifold "by Loring W.Tu . I am not understand this line "euclidean spaces are handicap because, defined in terms of coordinates, it is often not obvious which concepts are intrinsic, i.e., independent of coordinates" I am not understand which concept are intrinsic. ..Please any one help me to understand these line ..and explain in easy way

Answer 1

The Euclidean metric and many of its properties are ``intrinsic''. For example, for any two distinct points $x$ and $y$, there is a unique point $z$ such that $d(x,z)=d(z,y)=d(x,y)/2$. All the properties of lines you learned in high school (such as, two distinct lines cannot intersect in exactly 2 points) are intrinsic properties.