Latex / Tikz: draw a vertical line to a straight line - math

Question

Maybe you can help me, I try to draw a line from a Point/Coordinate to a straight line. I use Tikz to draw.
\begin{tikzpicture}
\coordinate [label=left:$A$] (A) at (-5,-5){};
\coordinate [label=right:$B$] (B) at (5,-5) {};
\coordinate [label=right:$C$] (C) at (5,1) {};
\coordinate [label=left:$D$] (D) at (-5,1) {};
\draw [thick] (A) -- node[midway] {$\parallel$} (B) -- node[sloped]{$\parallel$} (C) -- (D) -- cycle;
\coordinate (S1) at ($(D)!0.66!(C)$);
\coordinate (S2) at ($(A)!0.11!(B)$);
\draw [very thick] (S1) -- node[above]{x} (S2);
\draw [red!100, thick] (S1) -- node[above]{T} (A -| B );
\end{tikzpicture}
This where the red line should go
the red line should go from coordinate (S1) to the straight line (A -- B) vertically.
I tried it to draw it like this:
\draw [red!100, thick] (S1) -- node[above]{T} (A -| B );
But then he draw a line to coordinate A
Thank you,

Answer 1

You can do that by defining a new coordinate (say S3) for the point on AB:
\begin{tikzpicture}
\coordinate [label=left:$A$] (A) at (-5,-5){};
\coordinate [label=right:$B$] (B) at (5,-5) {};
\coordinate [label=right:$C$] (C) at (5,1) {};
\coordinate [label=left:$D$] (D) at (-5,1) {};
\draw [thick] (A) -- node[midway] {$\parallel$} (B) -- node[sloped]{$\parallel$} (C) -- (D) -- cycle;
\coordinate (S1) at ($(D)!0.66!(C)$);
\coordinate (S2) at ($(A)!0.11!(B)$);
\coordinate (S3) at ($(A)!0.66!(B)$);
\draw [very thick] (S1) -- node[above]{x} (S2);
\draw [red!100, thick] (S1) -- node[left]{T} (S3);
\end{tikzpicture}

Answer 2

You don't need to define a new coordinate but you can use the projection identifiers from calc library.
In the last line you just need
\draw [red!100, thick] (S1) -- node[left]{T} ($(A)!(S1)!(B)$);
This mean along A--B take the point which S1 is projected onto A--B.

Answer 3

Your syntax is nearly correct, but the tee operators |- and -| take the x coordinate from one side and the y coordinate from other. When you write
A -| B you get the y coordinate of A and the x coordinate of B, but in your code A and B have the same x coordinate so this gives you the point A again. Instead you want A -| S1, or equivalently S1 |- A.
\draw [red!100, thick] (S1) -- node[left]{T} (S1 |- A);
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\coordinate [label=left:$A$] (A) at (-5,-5){};
\coordinate [label=right:$B$] (B) at (5,-5) {};
\coordinate [label=right:$C$] (C) at (5,1) {};
\coordinate [label=left:$D$] (D) at (-5,1) {};
\draw [thick] (A) -- node[midway] {$\parallel$} (B) -- node[sloped]{$\parallel$} (C) -- (D) -- cycle;
\coordinate (S1) at ($(D)!0.66!(C)$);
\coordinate (S2) at ($(A)!0.11!(B)$);
\draw [very thick] (S1) -- node[above]{x} (S2);
\draw [red!100, thick] (S1) -- node[left]{T} (S1 |- A);
\end{tikzpicture}
\end{document}