documentclass{beamer}

% Note - to make this an article/handout we would use:
% documentclass{article}
% usepackage{beamerarticle}

usepackage{pgfpages}
usepackage{blindtext}
blindmathtrue
usepackage{multicol}
% setbeameroption{show notes on second screen}
usetheme[progressbar=frametitle]{metropolis}           % Use metropolis theme
% setbeamertemplate{frame numbering}[none]
metroset{block=fill}
setbeamercovered{transparent=15}

usepackage{amsmath,amssymb,amsthm,mathrsfs,bbm,bm}
usepackage{graphicx,subcaption,float,enumerate}


title[short title]{Functions Testing}
subtitle{Lecture 1}
date{}
author{}
institute{School}


begin{document}
maketitle
% setbeameroption{show notes on second screen}



begin{frame}[Tea]

begin{tikzpicture}[thick,help lines/.style={thin,draw=black!50}]

defA{textcolor{input}{$A$}} defC{textcolor{output}{$C$}} defE{$E$}

colorlet{input}{blue!80!black} colorlet{triangle}{orange}

defB{textcolor{input}{$B$}} defD{$D$}

colorlet{output}{red!70!black}

coordinate [label=left:A]

(A) at ($ (0,0) + .1*(rand,rand) $); coordinate [label=right:B] (B) at ($ (1.25,0.25) + .1*(rand,rand) $);

draw [input] (A) -- (B);

node [name path=D,help lines,draw,label=left:D]

node [name path=E,help lines,draw,label=right:E]

(D) at (A) [circle through=(B)] {};

(E) at (B) [circle through=(A)] {};

path [name intersections={of=D and E,by={[label=above:C]C}}];

draw [output] (A) -- (C) -- (B);

foreach point in {A,B,C} fill [black,opacity=.5] (point) circle (2pt);

begin{pgfonlayer}{background} fill[triangle!80] (A) -- (C) -- (B) -- cycle;

end{pgfonlayer}

node [below right, text width=10cm,align=justify] at (4,3) { smalltextbf{Proposition I}par emph{To construct an textcolor{triangle}{equilateral triangle} on a given textcolor{input}{finite straight line}.} parvskip1em Let AB be the given textcolor{input}{finite straight line}.

}; end{tikzpicture}

end{frame}

end{document}