diff --git a/04/pitagoras.pdf b/04/pitagoras.pdf new file mode 100644 index 0000000..437fc2b Binary files /dev/null and b/04/pitagoras.pdf differ diff --git a/04/pitagoras.tex b/04/pitagoras.tex new file mode 100644 index 0000000..2942354 --- /dev/null +++ b/04/pitagoras.tex @@ -0,0 +1,38 @@ + +\documentclass{beamer} +\usetheme{Berlin} +\usepackage[utf8]{inputenc} +\usepackage{polski} +\author{Grzegorz Adamski} +\usepackage{tikz} +\useinnertheme[shadow=true]{rounded} +\useoutertheme{infolines} +\usecolortheme{wolverine} +\setbeamercolor{alerted text}{fg=red} +\title[Pitagoras]{Dowód twierdzenia Pitagorasa} +\date{09.11.2017} +\begin{document} +\maketitle +\begin{frame}{This is dowód} +\begin{center} +\begin {tikzpicture} +\draw[blue] (0 ,0)--(1 ,2)--(5 ,0)--(0,0); +\draw[blue] (1 ,2)--(1,0); +\fill ( 5 , 0 ) circle[radius=2pt]; +\node [below right] at ( 5 , 0 ) {$B$}; +\fill ( 0 , 0 ) circle[radius=2pt] ; +\node [below right] at ( 0 , 0 ) {$A$}; +\fill ( 1 , 2 ) circle[radius=2pt] ; +\node [above right] at ( 1 , 2 ) {$C$}; +\fill ( 1 , 0 ) circle[radius=2pt] ; +\node [below right] at ( 1 , 0 ) {$D$}; +\end{tikzpicture} +\end{center} + +Trójkąty $ADC$, $BCD$ i $ABC$ są podobne, zatem $|AD|=a$, $|DC|=ab$, $|DB|=ab^2$, $|AC|=c$, $|BC|=cb$. Pole trójkąta $ABC$ jest równe sumie pól trójkątów $ADC$ i $BCD$, zatem: +\[\frac{a\cdot ab}{2}+\frac{ab\cdot ab^2}{2}=\frac{c\cdot cb}{2}.\] +Po skróceniu otrzymujemy: +\[a^2+b^2=c^2.\] +\end{frame} + +\end{document} \ No newline at end of file