如何从 tikzpikture 中删除空白

Question

我的图片中有空白。如何去除它们？

\documentclass{standalone}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}    
\tkzDefPoint(0,0){M}
\tkzDefPoint(5,0){N}
\tkzDrawTriangle[two angles= 120 and 20](M,N) \tkzGetPoint{P}
\tkzMarkAngles[size=0.8cm,arc=ll](P,N,M)
\tkzMarkAngles[size=0.8cm,arc=l](M,P,N)
\tkzLabelAngles[pos = 1.5](P,N,M){$20^{\circ}$}%
\tkzLabelAngles[pos = 1.2](M,P,N){$40^{\circ}$}%
\tkzLabelPoints[right](N)
\tkzLabelPoints[left](M)
\tkzLabelPoints[above](P)
\end{tikzpicture}
\end{document}

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[russian]{babel}
\usepackage{geometry}
\geometry{left=10 mm, top=10mm, right=15 mm }
\usepackage{multicol}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{calc}

\title{Sum of angles in triangle}
\author{ILDAR SHAYKHULIN}
\date{March 2020}

\begin{document}

\section*{\hfil Соотношения между сторонами и углами треугольника \hfil}
\subsection*{\hfil Задачи очень легкие \hfil}
\begin{enumerate}
    \item Напишите значение указаних величин, используя рисунки:

\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}

&\
\begin{tikzpicture}    

\end{tikzpicture} \\ 
\multicolumn{1}{c}{1.1} & \multicolumn{1}{c}{1.2} \\
\end{tabular}


\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
 \begin{tikzpicture}    
\tkzDefPoint(0,0){A}
\tkzDefPoint(5,0){B}
\tkzDrawTriangle[two angles= 45 and 35](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.8cm,arc=l](C,B,A)
\tkzMarkAngles[size=0.8cm,arc=ll](B,A,C)
\tkzLabelAngles[pos = 1.2](C,B,A){$35^{\circ}$}%
\tkzLabelAngles[pos = 1.2](B,A,C){$45^{\circ}$}%
\tkzLabelPoints[right](B)
\tkzLabelPoints[left](A)
\tkzLabelPoints[above](C)
\end{tikzpicture} &\ \begin{tikzpicture}    
\tkzDefPoint(0,0){A}
\tkzDefPoint(4.5,1){B}
\tkzDrawTriangle[two angles= 75 and 30](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.5cm,arc=ll](B,A,C)
\tkzLabelAngles[pos = 1](B,A,C){$75^{\circ}$}%
\tkzMarkSegments[mark=||,size=5 pt](B,A B,C)
\tkzLabelPoints[right](B)
\tkzLabelPoints[left](A)
\tkzLabelPoints[above](C)
\end{tikzpicture} \\
\multicolumn{1}{c}{1.3} & \multicolumn{1}{c}{1.4} \\
\end{tabular}

\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
 \begin{tikzpicture}    
\tkzDefPoint(0,0){A}
\tkzDefPoint(4,1){B}
\tkzDefPoint(-1,1){g}
\tkzDrawTriangle[two angles= 60 and 60](A,B) \tkzGetPoint{C}
\tkzMarkSegments[mark=||,size=5 pt](B,A B,C A,C)
\tkzLabelPoints[right](B)
\tkzLabelPoints[left](A)
\tkzLabelPoints[above](C)
\end{tikzpicture} &\ \begin{tikzpicture}    
\tkzDefPoint(0,0){A}
\tkzDefPoint(5.5,0){B}
\tkzDefPoint(7,0){F}
\tkzDrawLine (B,F)
\tkzDrawTriangle[two angles= 85 and 35](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.4cm,arc=l](F,B,C)
\tkzMarkAngles[size=0.8cm,arc=ll](B,A,C)
\tkzLabelAngles[pos = 0.8](F,B,C){$145^{\circ}$}%
\tkzLabelAngles[pos = 1.2](B,A,C){$45^{\circ}$}%
\tkzLabelPoints[below right](B)
\tkzLabelPoints[left](A)
\tkzLabelPoints[above](C)
\end{tikzpicture} \\
\multicolumn{1}{c}{1.5} & \multicolumn{1}{c}{1.6}\\
\end{tabular}

\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
 \begin{tikzpicture} [rotate=30]    
\tkzDefPoint(0,0){M}
\tkzDefPoint(0:4){N}
\tkzDefPoint(0:5){T}
\tkzDefPoint(180:1){F}
\tkzDefPoint(-1,0){A}
\tkzDrawLine (M,F)
\tkzDrawLine (N,T)
\tkzDrawTriangle[two angles= 90 and 25](M,N) \tkzGetPoint{P}
\tkzMarkRightAngle[](P,M,F)
\tkzMarkAngles[size=0.4cm,arc=ll](T,N,P)
\tkzLabelPoints[below right](N)
\tkzLabelPoints[below right](M)
\tkzLabelPoints[above](P)
\tkzLabelAngles[pos = 0.8](T,N,P){$155^{\circ}$}%
\end{tikzpicture} &\ \begin{tikzpicture}[rotate=130]      
\tkzDefPoint(0,0){A}
\tkzDefPoint(4.5,0){B}
\tkzDrawTriangle[two angles= 50 and 80](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.5cm,arc=ll](C,B,A)
\tkzLabelAngles(C,B,A){$80^{\circ}$}%
\tkzMarkSegments[mark=||,size=5 pt](B,A B,C)
\tkzLabelPoints[above](B)
\tkzLabelPoints[right](A)
\tkzLabelPoints[left](C)
\end{tikzpicture} \\
\multicolumn{1}{c}{1.7} & \multicolumn{1}{c}{1.8}\\
\end{tabular}

\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
 \begin{tikzpicture}   \tkzDefPoint(0,0){A}
\tkzDefPoint(4.5,0){B}
\tkzDefPoint(5.5,0){D}
\tkzDrawLine (B,D)
\tkzDrawTriangle[two angles= 67 and 46](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.5cm,arc=ll](D,B,C)
\tkzLabelAngles[pos = 1](D,B,C){$134^{\circ}$}%
\tkzMarkSegments[mark=||,size=5 pt](B,A B,C)
\tkzLabelPoints[below right](B)
\tkzLabelPoints[left](A)
\tkzLabelPoints[above](C) 
\end{tikzpicture}  &\ \begin{tikzpicture}    
    \tkzDefPoint(0,0){A}
\tkzDefPoint(4.5,0){B}
\tkzDefPoint(-1,0){D}
\tkzDrawLine (A,D)
\tkzDrawTriangle[two angles= 70 and 40](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.5cm,arc=ll](C,A,D)
\tkzLabelAngles[pos = 1](D,A,C){$140^{\circ}$}%
\tkzMarkSegments[mark=||,size=5 pt](B,A B,C)
\tkzLabelPoints[below right](B)
\tkzLabelPoints[below left](A)
\tkzLabelPoints[above](C) 
\end{tikzpicture} \\
\end{tabular}

\item Найдите угол $\angle C$ треугольника АВС, если: \\ 
a) $\angle A=65^\circ$, $\angle B=57^\circ$; \\ 
б)  $\angle A=24^\circ$, $\angle B=130^\circ$; \\
в)  $\angle A=\alpha$, $\angle B=2\alpha$; \\
г) $\angle A=60^\circ+\alpha$, $\angle B=60^\circ-\alpha$; \\

\item Докажите, что каждый угол равностороннего треугольника равен $ 60^\circ$.
\item Докажите, что углы при основании равнобедренного треугольника острые.


\subsection*{\hfil Задачи легкие \hfil}




\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
 \begin{tikzpicture}    
\tkzDefPoint(0,0){M}
\tkzDefPoint(0:3){N}
\tkzDefPoint(0:4){T}
\tkzDefPoint(-1,0){A}
\tkzDrawLine (N,T)
\tkzDrawTriangle[two angles= 90 and 45](M,N) \tkzGetPoint{P}
\tkzMarkAngles[size=0.4cm,arc=ll](T,N,P)
\tkzLabelPoints[below right](N)
\tkzLabelPoints[ left](M)
\tkzLabelPoints[above](P)
\tkzLabelAngles[pos = 0.8](T,N,P){$135^{\circ}$}%
\tkzMarkSegments[mark=||,size=5 pt](P,M M,N)
\tkzDefPointBy[projection = onto P--N](M) \tkzGetPoint{H}
\tkzDrawSegments (M,H)
\tkzMarkRightAngle[](M,H,N)
\tkzLabelPoints[above right](H)
\end{tikzpicture} &\ \begin{tikzpicture}  
\tkzDefPoint(0,0){A}
\tkzDefPoint(60:3){B}
\tkzDrawTriangle[two angles= 60 and 60](A,B) \tkzGetPoint{C}
\tkzLabelPoints[below](A)
\tkzLabelPoints[above](C)
\tkzLabelPoints[above](B)
\tkzDefLine[bisector](B,A,C) \tkzGetPoint{I}
\tkzInterLL(C,B)(A,I) \tkzGetPoint{D}
\tkzDrawSegments[](A,D)
\tkzLabelPoints[above](D)
\tkzMarkAngles[size=0.4cm,arc=ll](A,C,D)
\tkzLabelAngles[pos = 1](A,C,D){$60^{\circ}$}%
\tkzMarkRightAngle[](C,D,A)
\end{tikzpicture} \\
\end{tabular}

\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
\begin{tikzpicture}    
\tkzDefPoint(0,0){A}
\tkzDefPoint(4.5,1){B}
\tkzDrawTriangle[two angles= 75 and 30](A,B) \tkzGetPoint{C}
\tkzMarkAngles[size=0.5cm,arc=ll](B,A,C)
\tkzLabelAngles[pos = 1](B,A,C){$75^{\circ}$}%
\tkzMarkSegments[mark=||,size=5 pt](B,A B,C)
\tkzLabelPoints[right](B)
\tkzLabelPoints[left](A)
\tkzLabelPoints[above](C)
\end{tikzpicture} &\ \begin{tikzpicture}
\tkzDefPoint(0,0){M}
\tkzDefPoint(0:3){N}
\tkzDefPoint(180:1){T}
\tkzDefPoint(-1,0){H}
\tkzDrawLine (M,T)
\tkzDrawTriangle[two angles= 60 and 90](M,N) \tkzGetPoint{P}
\tkzMarkAngles[size=0.4cm,arc=ll](P,M,T)
\tkzLabelPoints[below right](N)
\tkzLabelPoints[ below left](M)
\tkzLabelPoints[above](P)
\tkzLabelAngles[pos = 0.8](P,M,T){$120^{\circ}$}%
\tkzDefLine[bisector](M,P,N) \tkzGetPoint{I}
\tkzInterLL(M,N)(P,I) \tkzGetPoint{D}
\tkzLabelPoints[below](D)
\tkzMarkAngles[size=0.9cm,arc=l](M,P,D)
\tkzMarkAngles[size=1cm,arc=l](D,P,N)
\tkzDrawSegments[](P,D)
\end{tikzpicture} \\ 
\end{tabular}

\begin{tabular}{p{0.45\textwidth}p{0.45\textwidth}}
 \begin{tikzpicture}    

\end{tikzpicture} &\ \begin{tikzpicture}    

\end{tikzpicture} \\
\end{tabular}

\begin{tabular}{p{0.45\textwidth}p{0.45\textwidth}}
 \begin{tikzpicture}    

\end{tikzpicture} &\ \begin{tikzpicture}    

\end{tikzpicture} \\
\end{tabular}

\begin{tabular}{p{0.45\textwidth}p{0.45\textwidth}}
 \begin{tikzpicture}    

\end{tikzpicture} &\ \begin{tikzpicture}    

\end{tikzpicture} \\
\end{tabular}
\subsection*{\hfil Задачи средние \hfil}
\begin{tabular}{p{0.45\textwidth}p{0.45\textwidth}}
 \begin{tikzpicture}    

\end{tikzpicture} &\ \begin{tikzpicture}    

\end{tikzpicture} \\
\end{tabular}
\item Найдите углы треугольника АВС, если $\angle A:\angle B:\angle C= = 2:3:4$.\\

\end{enumerate}
\end{document}

Answer 1

您可以使用overlay键从边界框中排除辅助路径。

\documentclass{standalone}
\usepackage{tikz}
\usepackage{tkz-euclide}
%\usetkzobj{all} %<- no longer needed, please update your TeX installation
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}    
\tkzDefPoint(0,0){M}
\tkzDefPoint(5,0){N}
\begin{scope}[overlay]
\tkzDrawTriangle[two angles= 120 and 20](M,N)
\tkzGetPoint{P}
\tkzMarkAngles[size=0.8cm,arc=ll](P,N,M)
\tkzMarkAngles[size=0.8cm,arc=l](M,P,N)
\tkzLabelAngles[pos = 1.5](P,N,M){$20^{\circ}$}%
\tkzLabelAngles[pos = 1.2](M,P,N){$40^{\circ}$}%
\end{scope}
\tkzLabelPoints[right](N)
\tkzLabelPoints[left](M)
\tkzLabelPoints[above](P)
\end{tikzpicture}
\end{document}

PS 据我所知%\usetkzobj{all}不再需要，请更新您的 TeX 安装。