File:Isosceles-triangle-more.svg
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Size of this PNG preview of this SVG file: 562 × 599 pixels. Other resolutions: 225 × 240 pixels | 450 × 480 pixels | 720 × 768 pixels | 960 × 1,024 pixels | 1,920 × 2,048 pixels | 900 × 960 pixels.
Original file (SVG file, nominally 900 × 960 pixels, file size: 11 KB)
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[edit]This file was created with LaTeX (TikZ), starting with my TikZ template:
\documentclass{article}
\usepackage{xcolor}
\definecolor{cWinkelhalbierende}{HTML}{00940A}
\definecolor{cSeitenhalbierende}{HTML}{FF0000}
\definecolor{cAchse}{HTML} {94008A}
\definecolor{cMittelsenkrechten}{HTML}{181FED}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{shapes, calc}
\begin{document}
\begin{preview}
\begin{tikzpicture}
\coordinate[label=left:$A$] (A) at (0,0);
\coordinate[label=right:$B$] (B) at (3.2,0);
\coordinate[label=left:$C$] (C) at (1.6,4);
% Draw the background of the triangle
\node[isosceles triangle, isosceles triangle apex angle=44,draw,
inner sep=0pt,anchor=lower side,rotate=90,draw=black,
line width=1.5pt, minimum height=4cm, fill=gray!2]
(triangle) at (1.6,-0.05) {};
% Rechte Winkel
\begin{scope}[shift={($(A)!0.5!(C)$)}, rotate=-22]
\draw[fill=gray!30] (0,0) -- (-180:0.25cm) arc (180:90:0.25cm);
\draw (140:0.15cm) node {$\cdot$};
\end{scope}
\begin{scope}[shift={($(B)!0.5!(C)$)}, rotate=-70]
\draw[fill=gray!30] (0,0) -- (-180:0.25cm) arc (180:90:0.25cm);
\draw (140:0.15cm) node {$\cdot$};
\end{scope}
\begin{scope}[shift={($(A)!0.5!(B)$)}]
\draw[fill=gray!30] (0,0) -- (-180:0.25cm) arc (180:90:0.25cm);
\draw (140:0.15cm) node {$\cdot$};
\end{scope}
% Mittelsenkrechten
% y = m * x + t
% Für die Mittelsenkrechte m_AB gilt ($(A)!0.5!(B)$) ist auf m_AB
% m = - (delta x) / (delta y) = - (A.x - B.x) / (A.y - B.y)
% t = y - m*x
% AB
\draw[color=cAchse, thick] (1.6cm,-0.3) -- node {} (1.6cm, 4.2cm);
% AC
% (0.8, 2) \in Mittelsenkrechte auf b
% m = - (-1.6)/(-4) = - 0.4
% t = 2 + 0.4 * 0.8 = 2.32
% y = -0.4 * x + 2.32
% (0, 2.32) und (3, 1.12)
\draw[color=cMittelsenkrechten] (0,2.32) -- node {} (3, 1.12);
% Umkreismittelpunkt
% x = 1.6
% y = -0.4*1.6 + 2.32 = 1.68
\node [circle,inner sep=1pt,fill=cMittelsenkrechten] at (1.6,1.68) {};
% ((3.2+1.6)/2, (0+4)/2) ) = (2.4, 2) \in Mittelsenkrechte auf a
% 2 = m * 2.4 + t
% m_BC = delta y / delta x = (0-4)/(3.2-1.6) = -2.5 = -5/2
% m = 2/5
% t = y - m*x = 2 - 2.4 * 2/5 = 1.04
% => y = 2/5 * x + 1.04
% (0, 1.04) und (3, 2.24)
\draw[color=cMittelsenkrechten] (0, 1.04) -- node {} (3, 2.24);
% Seitenhalbierende
\draw[color=cSeitenhalbierende,dashed] (A) -- node {} ($(B)!0.5!(C)$);
\draw[color=cSeitenhalbierende,dashed] (B) -- node {} ($(A)!0.5!(C)$);
%\draw[color=red, dashed] (C) -- node {} ($(A)!0.5!(B)$);
% Schwerpunkt
% x = 1.6
\node [circle,inner sep=1pt,fill=cSeitenhalbierende] at (1.6,1.34) {};
% Winkelhalbierende
% apex angle = 44° => alpha = 68° => 34°
\draw[color=cWinkelhalbierende, densely dashed] (A) -- node {} (34:4);
\begin{scope}[shift={($(B)$)}]
\draw (146:4) node (BEnd) {};
\end{scope}
\draw[color=cWinkelhalbierende, densely dashed] (B) -- node {} (BEnd);
%\draw[color=red, dashed] (C) -- node {} ($(A)!0.5!(B)$);
% Inkreismittelpunkt
% x = 1.6
% tan(68/2) = y/x => y = tan(34)*x = 1.48
\node [circle,inner sep=1pt,fill=cWinkelhalbierende] at (1.6,1.08) {};
% Draw the triangle
\node[isosceles triangle, isosceles triangle apex angle=44,draw,
inner sep=0pt,anchor=lower side,rotate=90,draw=black,
line width=1.5pt, minimum height=4cm]
(triangle) at (1.6,-0.05) {};
\end{tikzpicture}
\end{preview}
\end{document}
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 10:50, 17 June 2016 | 900 × 960 (11 KB) | MartinThoma (talk | contribs) | Remove black dash from right angle symbol | |
06:07, 14 June 2016 | 900 × 960 (11 KB) | MartinThoma (talk | contribs) | Update size | ||
07:11, 6 August 2012 | 164 × 175 (11 KB) | MartinThoma (talk | contribs) | Farbe der Winkelhalbierenden zu {{legend|#00940A|#00940A - 0, 148, 10}} gändert. | ||
15:21, 5 August 2012 | 164 × 175 (11 KB) | MartinThoma (talk | contribs) | Rechter Winkel bei AC korrigiert | ||
15:09, 5 August 2012 | 164 × 175 (11 KB) | MartinThoma (talk | contribs) | Besondere Punkte markiert | ||
08:27, 3 August 2012 | 164 × 175 (10 KB) | MartinThoma (talk | contribs) | Dreiecksfläche eingefärbt, Farben angepasst | ||
08:10, 3 August 2012 | 164 × 175 (9 KB) | MartinThoma (talk | contribs) | Winkelhalbierende eingezeichnet; Symmetrieachse betont; Beschriftung der Seiten und der Winkel entfernt. | ||
12:16, 2 August 2012 | 164 × 187 (18 KB) | MartinThoma (talk | contribs) | {{Information |Description ={{en|1=Isosceles triangle}} {{de|1=Gleichschenkliges Dreieck mit Seitenhalbierenden und Winkelhalbierenden}} |Source ={{own}} |Author =MartinThoma |Date =2012-08-02 |Permissi... |
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Width | 720pt |
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Height | 768pt |