Cómo usar tikz para dibujar polígonos con ángulos resaltados

Question

Estoy intentando replicar esta figura en látex. Obviamente es bastante fácil hacerlo en Geogebra... pero me preguntaba si hay algún paquete especial que podamos usar para hacer este tipo de figuras en látex. Muchas gracias de antemano.

Answer 1

yo asumo esoa, b, thetason dados.
Entonces así:

€dice:Con el 'ángulo recto agudo', que desea:

\draw pic [draw, angle radius=3mm, 
angle eccentricity=0.5, "$\cdot$",
] {right angle =C--P--D};

Tenga en cuenta que puede comentar angle eccentricity=0.5, "$\cdot$"si no desea un punto interior.

\documentclass[margin=5pt, tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{angles, quotes, babel}
\usepackage{amsmath, amssymb}

\begin{document}
\pgfmathsetmacro{\a}{4} %  
\pgfmathsetmacro{\b}{2.5} %  
\pgfmathsetmacro{\thetaA}{33} %  

\pgfmathsetmacro{\x}{\a*tan(\thetaA)} %  
\pgfmathsetmacro{\y}{\b/tan(\thetaA)} %  

\begin{tikzpicture}[%scale=0.7,
font=\footnotesize,
>={Triangle[length=0pt 9,width=0pt 4]}
]
\coordinate[label=left:$A$] (A) at (0,0); 
\coordinate[label=below:$B$] (B) at (\x+\y,0); 
\coordinate[label=left:$D$] (D) at (0,\a); 
\coordinate[label=below:$P$] (P) at (\x,0); 

\draw[] (A) -- (D) node[midway, left]{$a$};
\draw[] (A) -- (P) node[midway, below]{$x$};
\draw[] (P) -- (B) node[midway, below]{$y$};
\draw[] (B) -- +(0,\b) coordinate[label=right:$C$](C) node[midway, right]{$b$};

\draw[] (D) -- (P) node[midway, above]{$c$};
\draw[] (C) -- (P) node[midway, above]{$d$};
\draw[] (C) -- (D);

%% Angles
\draw pic [draw, angle radius=7mm, %angle eccentricity=1.3,
"$\theta$", ->
] {angle =A--D--P};
\draw pic [draw, angle radius=8mm, %angle eccentricity=1.3,
"$\theta$", ->
] {angle =P--D--C};
\draw pic [draw, angle radius=7mm, %angle eccentricity=1.3,
"$\theta$", ->
] {angle =B--P--C};
    
\draw pic [draw, angle radius=3mm, 
angle eccentricity=0.5, "$\cdot$",
] {right angle =C--P--D};
\draw pic [draw, angle radius=3mm, 
angle eccentricity=0.5, "$\cdot$",
] {right angle =P--A--D};
\draw pic [draw, angle radius=3mm, 
angle eccentricity=0.5, "$\cdot$",
] {right angle =C--B--P};

%% Points
\foreach \P in {P} \draw[fill=black!1] (\P) circle (1.75pt);

%% Annotations
\path[local bounding box=figure] (A) -- (B) -- (C) -- (D) --cycle;
\node[yshift=-5mm, draw, align=left, fill=lightgray!50,
anchor=north west,  % text width=\x cm+\y cm,
] at (figure.south west) {
$\begin{array}{l l}
a = \a \text{ cm}  &  \\
b = \b \text{ cm}  & \\ 
\theta = \thetaA^\circ   &  \\ \hline \\%[0.1em]
x = a\cdot\tan(\theta)   &  =\x  \text{ cm}    \\ 
y = \dfrac{b}{\tan(\theta)}   &  =\b \text{ cm} \hspace{2.0cm}\\
\end{array}$
};
\end{tikzpicture}
\end{document}

Answer 2

Para divertirte, un código pstricks que imita una construcción con regla y compás en una hoja de papel:

\documentclass[12pt, border=6pt, svgnames]{standalone}
\usepackage[upright]{fourier} 
\usepackage{pst-eucl}

\begin{document}

\begin{pspicture}(-0.1,-0.1)(5.2,4)
\psset{linestyle=none, PointSymbol=none, PointName=none}%
\pstGeonode(0,0){O}(0,4){B}(8,0){A}
\pstBissectBAC{O}{B}{A}{X} \pstInterLL{B}{X}{O}{A}{C}
\pstSymO{C}{B}[B1]
\pstMediatorAB{B}{B1}{C}{Y}\pstInterLL{A}{B}{C}{Y}{D}
\pstProjection{O}{A}{D}[E]
\psset{linestyle=solid, linejoin=1, linecolor=Coral}
\pspolygon(O)(B)(D)(E)
\psline(B)(C)(D)
%%angles
\psset{linecolor=black, linewidth=0.5pt}
\pstRightAngle[RightAngleSize=0.25]{B}{C}{D}
\psset{arrows=->,arrowinset=0.12, MarkAngleRadius=0.7}
\pstMarkAngle{C}{B}{D}{$\theta$}
\pstMarkAngle[MarkAngleRadius=0.8]{O}{B}{C}{$\theta$}
\pstMarkAngle{E}{C}{D}{$\theta$}
\end{pspicture}

\end{document}