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LaTeX 绘图轻松入门（第六集）- 向量和三角形
今天分享 TikZ 绘制向量与三角形，需要的可以直接复制获取使用。
概念解释：向量在数学中是一个重要的概念，也称为欧几里得向量或几何向量。它是指具有大小和方向的量，可以形象化地表示为带箭头的线段。箭头所指代表向量的方向，而线段长度则代表向量的大小。而三角形是一个基础的几何形状，它由三条线段（称为边）和三个角所构成。这三条边围成一个封闭的区域，三个角是这三条边相交所形成的。
一、向量
两向量夹角 (向量a,向量b)夹角为 φ
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning}
\tikzset{
%Define standard arrow tip
>=stealth',
% Define arrow style
pil/.style={->,thick}
}
\begin{document}
\begin{tikzpicture}
\draw[fill=green!30] (0,0) -- (90:.75cm) arc (90:27:.75cm);
\draw[pil,color=black] (0,0) -- node[right=2pt] {$\vec a$} (27:2.2cm);
\draw[pil,color=black] (0,0) -- node[near end, right=-3pt] {$\vec b$} (90:2cm);
\draw(60:0.5cm) node {$\varphi$};
\end{tikzpicture}
\end{document}
向量点积： a→⋅b→=|b→|cosφ
\begin{tikzpicture}
\draw[fill=gray!30] (27:0.90) -- node[right=-0.28cm, near end] {$\cdot$} (27:1.08)
arc (27:117:.18cm);
\draw[fill=green!30] (0,0) -- (90:.55cm) arc (90:27:.55cm);
\draw[pil,color=red] (0,0) -- node[right=2pt] {$\vec a$} (27:3cm);
\draw[pil,color=blue] (0,0) -- node[near end, right=-3pt] {$\vec b$} (90:2cm);
\draw[pil,color=violet] (0,0) -- node[near start, right=7pt] {$\vec b_{\vec a}$} (27:0.90cm);
\draw[color=gray, dashed] (27:0.90) -- node[near end, right] {} (90:2cm);
\draw(60:0.35cm) node {$\varphi$};
\end{tikzpicture}
向量的加减： a→−b→=c→
\begin{tikzpicture}[scale=0.8]
% draw the background
\draw [line width=0.1pt, fill=gray!2] (0,0) -- (3, 3) -- (5,0) -- cycle;
% angle gamma
\begin{scope}[shift={(3, 3)}]
\draw[fill=green!30] (0,0) -- (-135:.75cm) arc (-135:-55:.75cm);
\draw (-90:0.5cm) node {$\gamma$};
\end{scope}
\coordinate[label=left:$A$] (A) at (0,0);
\coordinate[label=right:$B$] (B) at (5,0);
\coordinate[label=above:$C$] (C) at (3,3);
\draw[arrow] (A) to[] node[below] {$\vec c$} (B);
\draw[arrow] (C) to[] node[above] {$\vec b$} (A);
\draw[arrow] (C) to[] node[above=0.1cm] {$\vec a$} (B);
\coordinate[label=+90:$c$] (c) at ($(A)!0.5!(B)$);
\coordinate[label=-120:$a$] (a) at ($(B)!0.5!(C)$);
\coordinate[label=-45:$b$] (b) at ($(C)!0.5!(A)$);
\end{tikzpicture}
向量分解
\begin{tikzpicture}
\draw[fill=gray!30] (27:0.90) -- node[right=-0.28cm, near end] {$\cdot$} (27:1.08)
arc (27:117:.18cm);
\draw[fill=green!30] (0,0) -- (90:.55cm) arc (90:27:.55cm);
\draw[pil,color=red] (0,0) -- node[right=2pt] {$\vec a$} (27:3cm);
\draw[pil,color=blue] (0,0) -- node[near end, right=-3pt] {$\vec b$} (90:2cm);
\draw[pil,color=violet] (0,0) -- node[near start, right=7pt] {$\vec b_{\vec a}$} (27:0.90cm);
\draw[color=gray, dashed] (27:0.90) -- node[near end, right] {} (90:2cm);
\draw(60:0.35cm) node {$\varphi$};
\end{tikzpicture}
二、三角形
三角形内角和： α+β+γ=π
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning, calc}
\begin{document}
\begin{tikzpicture}[scale=0.8]
% draw the background
\draw [line width=1.5pt, fill=gray!2] (0,0) -- (60:4) -- (4,0) -- cycle;
\coordinate[label=left:$A$] (A) at (0,0);
\coordinate[label=right:$B$] (B) at (4,0);
\coordinate[label=above:$C$] (C) at (2,3.464);
\coordinate[label=below:$c$](c) at ($ (A)!.5!(B) $);
\coordinate[label=left:$b$] (b) at ($ (A)!.5!(C) $);
\coordinate[label=right:$a$](a) at ($ (B)!.5!(C) $);
% angle alpha
\draw[fill=green!30] (0,0) -- (0:0.75cm) arc (0:60:.75cm);
\draw (0.35cm,0.25cm) node {$\alpha$};
% angle beta
\begin{scope}[shift={(4cm,0cm)}]
\draw[fill=green!30] (0,0) -- (-180:0.75cm) arc (180:120:0.75cm);
\draw (150:0.5cm) node {$\beta$};
\end{scope}
% angle gamma
\begin{scope}[shift={(60:4)}]
\draw[fill=green!30] (0,0) -- (-120:.75cm) arc (-120:-60:.75cm);
\draw (-90:0.5cm) node {$\gamma$};
\end{scope}
% the triangle
\draw [line width=1.5pt] (A) -- (B) -- (C) -- cycle;
\end{tikzpicture}
\end{document}
三角形外接圆和内切圆
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc, shapes.misc}
\tikzset{
%Define standard arrow tip
>=stealth',
% Define arrow style
pil/.style={->,thick}
}
\tikzstyle{point}=[ thick,
draw=gray,
cross out,
inner sep=0pt,
minimum width=4pt,
minimum height=4pt]
\begin{document}
\begin{tikzpicture}
% draw the background
% -2/cos(30°) = 4/sqrt(3) \approx 2.309 - Umkreisradius
% 2*tan(30°) = 2/sqrt(3) \approx 1.155 - Inkreisradius
\node[point] (TriangleCenter) at (0,0) {};
\draw[thick, draw=blue] (TriangleCenter) circle(2.345cm);
\begin{scope}[shift={(30:-2.309)}]
\draw [line width=1.5pt, fill=gray!2] (0,0) -- (60:4) -- (4,0) -- cycle;
\draw[thick, draw=green] (TriangleCenter) circle(1.12cm);
\coordinate[label=left:$A$] (A) at (0,0);
\coordinate[label=right:$B$] (B) at (4,0);
\coordinate[label=above:$C$] (C) at (2,3.464);
% Sign for right angle of h_c
%\begin{scope}[shift={(2,0)}]
% \draw[fill=gray!30] (0,0) -- node[above=-0.15cm,near start] {$\cdot$} (0:0.18cm)
% arc (0:90:.18cm);
%\end{scope}
% sign of right angle of h_a
%\begin{scope}[shift={(30:3.464cm)}]
% \draw[fill=gray!30] (0,0) -- node[near end,right=-0.28cm] {$\cdot$} (-60:0.18cm)
% arc (-60:-150:.18cm);
%\end{scope}
% sign of right angle of h_b
%\begin{scope}[shift={(60:2cm)}]
% \draw[fill=gray!30] (0,0) -- node[right=-0.08cm, near start] {$\cdot$} (60:0.18cm)
% arc (60:-30:.18cm);
%\end{scope}
% angle alpha
%\draw[fill=green!30] (0,0) -- (0:0.75cm) arc (0:60:.75cm);
%\draw (0.35cm,0.25cm) node {$\alpha$};
% angle beta
\begin{scope}[shift={(4cm,0cm)}]
%\draw[fill=green!30] (0,0) -- (-180:0.75cm) arc (180:120:0.75cm);
\draw[color=gray, dashed] (0,0) -- node[sloped, above=-0.1cm] {} (150:3.464cm); % $\scriptstyle h_b$
%\draw (150:0.5cm) node {$\beta$};
\end{scope}
% angle gamma
\begin{scope}[shift={(60:4)}]
%\draw[fill=green!30] (0,0) -- (-120:.75cm) arc (-120:-60:.75cm);
\draw[color=gray, dashed] (0,0) -- node[right=-0.1cm] {} (-90:3.464cm); % $\scriptstyle h_c$
%\draw (-90:0.5cm) node {$\gamma$};
\end{scope}
% Height with label
\draw[color=gray, dashed] (0,0) -- node[sloped, above=-0.1cm] {} (30:3.464cm); % $\scriptstyle h_a$
% The triangle
\draw [line width=1.5pt] (0,0) -- (60:4) -- (4,0) -- cycle;
\end{scope}
\coordinate[label=below:$c$](c) at ($ (A)!.5!(B) $);
\coordinate[label=left:$b$] (b) at ($ (A)!.5!(C) $);
\coordinate[label=right:$a$](a) at ($ (B)!.5!(C) $);
\end{tikzpicture}
\end{document}
三角形的垂心
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc}
\tikzset{
%Define standard arrow tip
>=stealth',
% Define arrow style
pil/.style={->,thick}
}
\begin{document}
\begin{tikzpicture}
% draw the background
\draw [line width=1.5pt, fill=gray!2] (0,0) -- (60:4) -- (4,0) -- cycle;
\coordinate[label=left:$A$] (A) at (0,0);
\coordinate[label=right:$B$] (B) at (4,0);
\coordinate[label=above:$C$] (C) at (2,3.464);
\coordinate[label=below:$c$](c) at ($ (A)!.5!(B) $);
\coordinate[label=left:$b$](b) at ($ (A)!.5!(C) $);
\coordinate[label=right:$a$](a) at ($ (B)!.5!(C) $);
% angle alpha
\draw[fill=green!30] (0,0) -- (0:0.75cm) arc (0:60:.75cm);
% angle beta
\begin{scope}[shift={(4cm,0cm)}]
\draw[fill=green!30] (0,0) -- (-180:0.75cm) arc (180:120:0.75cm);
\draw[color=gray, dashed] (0,0) -- node[sloped, above=-0.1cm] {$\scriptstyle h_b$} (150:3.464cm);
\end{scope}
% angle gamma
\begin{scope}[shift={(60:4)}]
\draw[fill=green!30] (0,0) -- (-120:.75cm) arc (-120:-60:.75cm);
\draw[color=gray, dashed] (0,0) -- node[right=-0.1cm] {$\scriptstyle h_c$} (-90:3.464cm);
\draw (-90:0.5cm) node {$\gamma$};
\end{scope}
% Sign for right angle of h_c
\begin{scope}[shift={(2,0)}]
\draw[fill=gray!30] (0,0) -- node[above=-0.15cm,near start] {$\cdot$} (0:0.18cm)
arc (0:90:.18cm);
\end{scope}
% sign of right angle of h_a
\begin{scope}[shift={(30:3.464cm)}]
\draw[fill=gray!30] (0,0) -- node[near end,right=-0.28cm] {$\cdot$} (-60:0.18cm)
arc (-60:-150:.18cm);
\end{scope}
% sign of right angle of h_b
\begin{scope}[shift={(60:2cm)}]
\draw[fill=gray!30] (0,0) -- node[right=-0.08cm, near start] {$\cdot$} (60:0.18cm)
arc (60:-30:.18cm);
\end{scope}
% Height with label
\draw[color=gray, dashed] (0,0) -- node[sloped, above=-0.1cm] {$\scriptstyle h_a$} (30:3.464cm);
\draw (0.35cm,0.25cm) node {$\alpha$};
\begin{scope}[shift={(4cm,0cm)}]
\draw (150:0.5cm) node {$\beta$};
\end{scope}
\begin{scope}[shift={(60:4)}]
\draw (-90:0.5cm) node {$\gamma$};
\end{scope}
% The triangle
\draw [line width=1.5pt] (0,0) -- (60:4) -- (4,0) -- cycle;
\end{tikzpicture}
\end{document}
三角形内角和证明
\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{tkz-euclide}
\usetikzlibrary{shapes, calc, shapes, decorations}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{preview}
\begin{tikzpicture}[thick]
\newcommand\XC{4}
\newcommand\ALPHA{30}
\newcommand\XB{{(\XC*(cos(\ALPHA)*cos(\ALPHA) - sin(\ALPHA)*sin(\ALPHA)) + \XC)*0.5}}
\newcommand\YB{{sqrt(cos(\ALPHA)*\XC*cos(\ALPHA)*\XC - (\XC*(cos(\ALPHA)*cos(\ALPHA) - sin(\ALPHA)*sin(\ALPHA)) + \XC)*0.5*(\XC*(cos(\ALPHA)*cos(\ALPHA) - sin(\ALPHA)*sin(\ALPHA)) + \XC)*0.5)}}
\newcommand\XBo{{(\XB)+4}}
\newcommand\YBo{{\YB}}
\newcommand\XBp{{\XB*0.5}}
\newcommand\YBp{{\YB*0.5}}
% Draw the triangle
\draw[fill=gray!10] (0, 0) coordinate (A)
-- (\XB,\YB) coordinate (C)
-- (\XC, 0) coordinate (B)
-- (0, 0) -- cycle;
% Draw nodes
\node at (A)[anchor=north] {A};
\node at (B)[anchor=north] {B};
\node at (C)[anchor=south] {C};
% Draw edge text
\node (c) at ($(A)!0.5!(B)$) [below] {c};
\node (b) at ($(A)!0.5!(C)$) [above] {b};
\node (a) at ($(B)!0.6!(C)$) [right] {a};
% draw alpha
\draw[fill=blue!30] (0,0) -- (0:0.75cm) arc (0:\ALPHA:.75cm);
\coordinate[label=right:$\alpha$] (Alpha) at (0.25,0.15);
% draw beta
\begin{scope}[shift={(\XC, 0)}]
\draw[fill=green!30] (0,0) -- (-180:0.50cm) arc (180:{180-(90-\ALPHA)}:0.5cm);
\draw (150:0.35cm) node {$\beta$};
\end{scope}
% draw gamma
\begin{scope}[shift={(\XB, \YB)}]
\draw[fill=red!30] (0,0) -- ({180+\ALPHA}:0.5cm) arc ({180+\ALPHA}:{180+\ALPHA+90}:0.5cm);
\draw (-0.1, -0.05) node[below] {$\gamma$};
\end{scope}
% shifted alpha
\begin{scope}[shift={(4,0)}]
\path[fill=blue!30] (0,0) -- (0:0.5cm) arc (0:\ALPHA:.5cm);
\draw (0:0.5cm) arc (0:\ALPHA:.5cm);
\end{scope}
% shifted gamma
\begin{scope}[shift={(4, 0)},rotate=180]
\path[fill=red!30] (0,0) -- ({180+\ALPHA}:0.5cm) arc ({180+\ALPHA}:{180+\ALPHA+90}:0.5cm);
\draw ({180+\ALPHA}:0.5cm) arc ({180+\ALPHA}:{180+\ALPHA+90}:0.5cm);
\end{scope}
\begin{scope}[shift={(3.13,-0.5)},scale=0.7]
\draw[dashed, red] (0, 0) -- (\XB,\YB);
\end{scope}
\draw[dashed, color=red] (-0.6, 0) -- (5.3, 0);
\draw (0, 0) coordinate (X)
-- (\XB,\YB) coordinate (Y)
-- (\XC, 0) coordinate (Z)
-- (0, 0);
\node at ( $ (A)!-0.2!(C) $ ) (helper11) {};
\node at ( $ (A)!0.1!(C) $ ) (helper12) {};
\node at ( $ (A)!0.6!(C) $ ) (helper2) {};
\node at ( $ (C)!-0.2!(A) $ ) (helper3) {};
\tkzDrawLine[thick,dashed](helper12,helper11)
\tkzDrawLine[thick,dashed](helper2, helper3)
\end{tikzpicture}
\end{preview}
\end{document}
三角形的一个外角等于其不相邻的内角之和
\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{shapes, calc, decorations}
\usepackage{amsmath,amssymb}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}
\begin{document}
\begin{preview}
\begin{tikzpicture}[very thick,font=\sansmath\sffamily]
\tkzDefPoint(0.7,3){A}
\tkzDefPoint(0,0){B}
\tkzDefPoint(3.2,0){C}
\tkzDefPoint(4.0,0){D}
\tkzLabelPoints[above,font=\sansmath\sffamily](A)
\tkzLabelPoints[below left,font=\sansmath\sffamily](B)
\tkzLabelPoints[below,font=\sansmath\sffamily](C)
% \tkzLabelPoints[below,font=\sansmath\sffamily](D)
% Draw polygon
\tkzDrawPolygon[fill=gray!10](A,B,C)
% Mark angles
\tkzMarkAngle[arc=l,size=0.6cm,fill=green!30](B,A,C)
\tkzLabelAngle[pos=0.3](B,A,C){$\alpha$}
\tkzMarkAngle[arc=l,size=0.6cm,fill=green!30](C,B,A)
\tkzLabelAngle[pos=0.4](C,B,A){$\beta$}
\tkzMarkAngle[arc=l,size=0.6cm,fill=green!30](A,C,B)
\tkzLabelAngle[pos=0.4](A,C,B){$\gamma$}
\tkzMarkAngle[arc=l,size=0.6cm,fill=red!30](D,C,A)
\tkzLabelAngle[pos=0.4](D,C,A){$\gamma'$}
\tkzDrawLines(B,D)
% Draw polygon
\tkzDrawPolygon(A,B,C)
% Make dots for points
\tkzDrawPoints[size=1.0](A,B,C)
\end{tikzpicture}
\end{preview}
\end{document}
三角形外角和为 2π
\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usepackage{tkz-euclide}
%\usetkzobj{all}
\usetikzlibrary{shapes, calc, decorations}
\usepackage{amsmath,amssymb}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}
\begin{document}
\begin{preview}
\begin{tikzpicture}[very thick,font=\sansmath\sffamily]
\tkzDefPoint(-1,-1){A}
\tkzDefPoint(3.2,0){B}
\tkzDefPoint(0.7,3){C}
\tkzDefBarycentricPoint(A=-5,C=1)
\tkzGetPoint{D}
\tkzDefBarycentricPoint(C=1,B=-5)
\tkzGetPoint{E}
\tkzDefBarycentricPoint(A=1,C=-5)
\tkzGetPoint{F}
\tkzLabelPoints[below left,font=\sansmath\sffamily](A)
\tkzLabelPoints[above right,font=\sansmath\sffamily](B)
\tkzLabelPoints[above=0.3,font=\sansmath\sffamily](C)
% \tkzLabelPoints[below,font=\sansmath\sffamily](D)
% Draw polygon
\tkzDrawPolygon[fill=gray!10](A,B,C)
% Mark angles
\tkzFillAngle[size=0.7,fill=green!30, opacity=0.5](B,A,C)
\tkzMarkAngle[size=0.7](B,A,C)
\tkzLabelAngle[pos=0.3](B,A,C){$\alpha$}
\tkzFillAngle[size=0.7,fill=green!30, opacity=0.5](C,B,A)
\tkzMarkAngle[size=0.7](C,B,A)
\tkzLabelAngle[pos=-0.4](C,B,A){$\beta$}
\tkzFillAngle[size=0.7,fill=green!30, opacity=0.5](A,C,B)
\tkzMarkAngle[size=0.7](A,C,B)
\tkzLabelAngle[pos=0.4](A,C,B){$\gamma$}
\tkzFillAngle[size=0.7,fill=red!30, opacity=0.5](D,A,B)
\tkzMarkAngle[size=0.7](D,A,B)
\tkzLabelAngle[pos=0.4](B,A,D){$\alpha'$}
\tkzFillAngle[size=0.7,fill=red!30, opacity=0.5](A,B,E)
\tkzMarkAngle[size=0.7](A,B,E)
%\tkzMarkAngle[size=0.7][arc=l,size=0.6cm,fill=red!30](A,B,E)
\tkzLabelAngle[pos=0.4](A,B,E){$\beta'$}
\tkzFillAngle[size=0.7,fill=red!30, opacity=0.5](B,C,F)
\tkzMarkAngle[size=0.7](B,C,F)
%\tkzMarkAngle[size=0.7][arc=l,size=0.6cm,fill=red!30](B,C,F)
\tkzLabelAngle[pos=0.4](B,C,F){$\gamma'$}
% \tkzMarkAngle[size=0.7][arc=l,size=0.6cm,fill=orange!30](D,C,A)
% \tkzLabelAngle[pos=0.4](D,C,A){$\delta$}
\tkzDrawLines(A,B B,C C,A)
% Label lines
% \tkzLabelSegment[below](A,B){$c$}
% \tkzLabelSegment[left](A,C){$b$}
% \tkzLabelSegment[right](B,C){$a$}
% Draw polygon
% \tkzDrawPolygon[thick](A,B,C)
% Make dots for points
\tkzDrawPoints[size=1.0](A,B,C)
\end{tikzpicture}
\end{preview}
\end{document}
直角三角形的各个参数指示
\documentclass{article} % or another class
\usepackage{xcolor} % before tikz or tkz-euclide if necessary
\usepackage{tkz-euclide} % no need to load TikZ
\begin{document}
\begin{tikzpicture}[scale=1.0]
%define points A,B,C
\tkzDefPoint(0,0){C}
\tkzDefPoint(20:9){B}
\tkzDefPoint(80:5){A}
%label point A,B,C
\tkzLabelPoints(B,C)
\tkzLabelPoints[above](A)
%draw triangleABC
\tkzDrawPolygon[thick,fill=yellow!15](A,B,C)
%get line orthogonal to base CB
\tkzDefPointsBy[projection=onto B--C](A){a}
\tkzDrawSegment[dashed, red](A,a)
%marking right angles
\tkzMarkRightAngle(A,a,C)
\tkzMarkRightAngle(C,A,B)
%drawing dimension 10
\tkzDrawSegment[style=red, dashed, dim={$10$,15pt,midway,font=\scriptsize, rotate=90}](A,a)
%marking the angles
\tkzFillAngle[fill=blue!20, opacity=0.5](B,C,A)
\tkzLabelAngle[pos=1.25](B,C,A){$\alpha$}
\tkzMarkAngle(B,C,A)
\tkzFillAngle[fill=red!20, opacity=0.5](A,B,C)
\tkzLabelAngle[pos=1.25](A,B,C){$\beta$}
\tkzMarkAngle(A,B,C)
\tkzDrawPoints(A,B,C)
\end{tikzpicture}
\end{document}
再来一个三角形
\documentclass{standalone}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usepackage{siunitx}
\usepackage{fourier}
\begin{document}
\begin{tikzpicture}
\tkzInit[xmin=-3,xmax=4.5, ymin=-.5, ymax=2.8]
\tkzClip
\tkzDefPoint(0,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(130:3){C}
\tkzDefLine[orthogonal=through C](A,B)\tkzGetPoint{c}
\tkzInterLL(A,B)(C,c)\tkzGetPoint{C'}
\tkzMarkAngle[size=.5,arrows=->,>=stealth,color=red](B,A,C)
\tkzMarkAngle[size=.4,arrows=->,>=stealth,color=blue](C,A,C')
\tkzMarkRightAngle[size=.3,fill=blue!20,draw opacity=0](A,C',C)
\tkzDrawSegment[dashed](C,C')
\tkzDrawLine[add=0cm and 1cm,dashed](A,C')
\tkzDrawPolygon(A,B,C)
\tkzDrawPoints(A,B,C,C')
\tkzLabelPoints[below](A,C')
\tkzLabelPoints[right](B)
\tkzLabelPoints[above](C)
\begin{scope}[font=\footnotesize]
\tkzLabelSegment[below](A,B){$c$}
\tkzLabelSegment(A,C){$b$}
\tkzLabelSegment[above](B,C){$a$}
\tkzLabelSegment[left](C,C'){$h$}
\tkzLabelAngle[pos=.7](B,A,C){$\widehat{A}$}
\tkzLabelAngle[pos=1.1,below](C,A,C'){$\ang{180}-\widehat{A}$}
\end{scope}
\end{tikzpicture}
\end{document}
入门资料，免费知识代码：
https://flowus.cn/latex/share/66110e84-b24a-4cd5-b8a7-2ba2afb35a30
精心制作免费视频教程：
https://space.bilibili.com/209746320