Insertion of perpendicular symbol at intersection of two perpendicular lines

Question

This provides good details on How to draw a line passing through a point and perpendicular to another?. What I would like to do is to extend this somehow to add the usual geometry symbol to indicate that the two lines are indeed perpendicular. I could code a manual solution for each situation, but would like a macro, one that would draw it of an appropriate size, and allow me to choose the orientation (i.e., select one of the four quadrants) for this symbol.

Answer 1

Here's one possible approach that uses a TikZ style. You insert the angle symbol by using the style

right angle symbol={<Point 1>}{<Point 2>}{<Point 3>}

in a draw command. If you want the angle symbol on its own, just use it in a new draw command:

\draw [right angle symbol={<Point 1>}{<Point 2>}{<Point 3>}];

The quadrant can be selected by using right angle quadrant=<1-4>, the size by using right angle length=<length>. Both these options have to be called before right angle symbol.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}

\tikzset{
    right angle quadrant/.code={
        \pgfmathsetmacro\quadranta{{1,1,-1,-1}[#1-1]}     % Arrays for selecting quadrant
        \pgfmathsetmacro\quadrantb{{1,-1,-1,1}[#1-1]}},
    right angle quadrant=1, % Make sure it is set, even if not called explicitly
    right angle length/.code={\def\rightanglelength{#1}},   % Length of symbol
    right angle length=2ex, % Make sure it is set...
    right angle symbol/.style n args={3}{
        insert path={
            let \p0 = ($(#1)!(#3)!(#2)$) in     % Intersection
                let \p1 = ($(\p0)!\quadranta*\rightanglelength!(#3)$), % Point on base line
                \p2 = ($(\p0)!\quadrantb*\rightanglelength!(#2)$) in % Point on perpendicular line
                let \p3 = ($(\p1)+(\p2)-(\p0)$) in  % Corner point of symbol
            (\p1) -- (\p3) -- (\p2)
        }
    }
}

\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
  extended line/.style={shorten >=-#1,shorten <=-#1},
  extended line/.default=1cm]

\node [dot=A] at (0,0) {};
\node [dot=B] at (3,1) {};
\node [dot=P] at (0.9,-1.2) {};
\node [dot=Q] at (1.3,2.2) {};

\draw [extended line=0.5cm] (A) -- (B);
\draw [extended line] ($(A)!(P)!(B)$) -- (P);


\draw [red,right angle symbol={A}{B}{P}];

\draw [extended line,right angle quadrant=3,right angle symbol={A}{B}{Q}] ($(A)!(Q)!(B)$) -- (Q);
\end{tikzpicture}
\end{document}

Answer 2

Another possibility is to use my package tkz-euclide (now on ctan and texlive 2011) but you don't need to get all the objects that I defined. Only angles are necessary. I take the Jake's example to show you that you can mix tikz and tkz. \usetkzobj{angles} this macro loads all the macros for the angles, if you need other objects \usetkzobj{angles,polygons} the syntax is the same as \usetikzlibrary and if you want all the objects , you write \usetkzobj{all}

\documentclass{article}
\usepackage{tkz-euclide} % loads  TikZ and tkz-base
\usetkzobj{angles} % important you want to use angles
\begin{document}

\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
  extended line/.style={shorten >=-#1,shorten <=-#1},
  extended line/.default=1cm]
\node [dot=A] at (0,0) {};
\node [dot=B] at (3,1) {};
\node [dot=P] at (0.9,-1.2) {};

%\draw [extended line=0.5cm] (A) -- (B);
% In tkz-euclide I defined something like extend line 
% but I prefer my method because I add a percentage of the segment  at each sides
% with [add = % and %] left and right 
\tkzDrawLine[add=1 and .5](A,B) % with 1 you double the line BA from A
\draw [extended line] ($(A)!(P)!(B)$) coordinate (H) -- (P);
 % I named the projection H
  \tkzMarkRightAngle[fill=blue!20,size=.5](A,H,P) % size number in cm
  % and you need to give the points in an order counterclockwise
  \tkzMarkRightAngle[fill=red!20,size=.8](B,H,P)  
\end{tikzpicture}  

% Now an example with only tkz-euclide
\begin{tikzpicture}[scale=.5]
  \tkzDefPoint(0,0){A}
  \tkzDefPoint(4,2.5){B}
  \tkzDefPoint(4,5){C}
  \tkzDrawLine[add= 0.5 and 0.8,color=blue](A,B)
   \tkzDefPointBy[projection=onto B--A](C)  \tkzGetPoint{H}
  \tkzDrawLine[add = .5 and .2,color=red](C,H)
  \tkzLabelPoint(H){$h$} 
  \tkzMarkRightAngle[fill=blue!20,size=.5](C,H,B)
  \tkzDrawPoints(A,B,C)\tkzLabelPoints(A,B,C) % better now
\end{tikzpicture}  

\end{document}