1) tkz-euclide
is on CTAN but not on TexLive I need to upload the sources of the documentation.
2) The solution with calc
it's not effective. The next code is from the pgfmanual
and I make a zoom on the intersection
(see The Syntax of Projection Modifiers)
\begin{tikzpicture} \draw [help lines] (0,0) grid (3,2);
\coordinate (a) at (0,1);
\coordinate (b) at (3,2);
\coordinate (c) at (2.5,0);
\draw (a) -- (b) -- (c) -- cycle;
\draw[red] (a) -- ($(b)!(a)!(c)$);
\draw[orange] (b) -- ($(a)!(b)!(c)$);
\draw[blue] (c) -- ($(a)!(c)!(b)$);
\end{tikzpicture}

On some cases, It's impossible to draw geometric picture without errors.
In tkz-euclide
, if I want a line from A perpendicular to BC, I define a vector BE perpendicular BC, then a vector AD perpendicular to BC and then I search the intersection of
AD and BC
3) For the extend style, another solution is :
\tikzset{%
add/.style args={#1 and #2}{
to path={%
($(\tikztostart)!-#1!(\tikztotarget)$)--($(\tikztotarget)!-#2!(\tikztostart)$)%
\tikztonodes}}
}
example : the idea is to use percentage add = 1 and 0, double the line, with 1 and 1 we get the triple, and you can use negative numbers
\documentclass[a4paper]{scrartcl}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,
fill,label={#1},name=#1},]
\tikzset{%
add/.style args={#1 and #2}{to path={%
($(\tikztostart)!-#1!(\tikztotarget)$)--($(\tikztotarget)!-#2!(\tikztostart)$)%
\tikztonodes}}
}
\node [dot=A](A) at (0,0) {};
\node [dot=B](B) at (3,1) {};
\node [dot=C](C) at (3,-1) {};
\draw[add = 1 and 0] (A) to (B);
\draw[add = .5 and .5] (A) to (C);
\end{tikzpicture}
\end{document}

shorten >=-1cm,shorten <=-1cm
together with a pseudo-arrow tip to extend the lines.shorten
(note spelling mistake in your comment) keys work independently of arrow tips so it's not necessary to specify an arrow tip. Thus\draw[shorten >=-1cm] (0,0) -- (2,0);
will work.