documentclass[10pt]{article}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage{pgf,tikz}
usepackage{tkz-tab}
 usetikzlibrary{shapes,snakes,arrows,backgrounds}
usetikzlibrary{scopes,svg.path,shapes.geometric,shadows}
usepackage{graphicx}
usepackage{xcolor}
begin{document}
begin{tikzpicture}[xscale=1.5, yscale=1.5]

draw [->](0,0,0) -- (3,0,0) node[anchor=west]{$y$};
draw [->, dashed](0,0,0) -- (0,3,0) node[anchor=west]{$z$};
draw [->](0,0,0) -- (0,0,3) node[anchor=west]{$x$};
draw [thick](1, 0, 0)--(0, 1, 0) -- (0, 0, 1)--(1, 0, 0);
fill [blue!50!gray!30] (1, 0, 0)--(0, 1, 0) -- (0, 0, 1)--(1, 0, 0);
draw (1, 0, 0) node[below] {$1$};
draw (0, 1, 0) node[left] {$1$};
draw (0, 0, 1) node[below] {$1$};
end{tikzpicture}
end{document}

begin{tikzpicture}[xscale=1.5, yscale=1.5,rotate=45]

documentclass[10pt]{article}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage{pgf,tikz}
usepackage{tkz-tab}
 usetikzlibrary{shapes,snakes,arrows,backgrounds}
usetikzlibrary{scopes,svg.path,shapes.geometric,shadows}
usepackage{graphicx}
usepackage{xcolor}
begin{document}
begin{tikzpicture}[xscale=1.5, yscale=1.5]
  fill [blue!50!gray!30] (1, 0, 0)--(0, 1, 0) -- (0, 0, 1)--(1, 0, 0);
  draw [->](0,0,0) -- (3,0,0) node[anchor=west]{$y$};
  draw [->, dashed](0,0,0) -- (0,3,0) node[anchor=west]{$z$};
  draw [->](0,0,0) -- (0,0,3) node[anchor=west]{$x$};
  draw [thick](1, 0, 0)--(0, 1, 0) -- (0, 0, 1)--(1, 0, 0);
  draw (1, 0, 0) node[below] {$1$};
  draw (0, 1, 0) node[left] {$1$};
  draw (0, 0, 1) node[below] {$1$};
end{tikzpicture}

end{document}

begin{tikzpicture}[xscale=1.5, yscale=1.5]
  draw[thick,fill=blue!50!gray!30] (1, 0, 0)node[below right]{$1$}
                 --(0, 1, 0)node[above left]{$1$}
                 --(0, 0, 1)node[below right]{$1$}--cycle;
  draw [->](0,0,0) -- (3,0,0) node[anchor=west]{$y$};
  draw [->, dashed](0,0,0) -- (0,3,0) node[anchor=west]{$z$};
  draw [->](0,0,0) -- (0,0,3) node[anchor=west]{$x$};
end{tikzpicture}

documentclass[10pt]{article}
usepackage{tikz}
usepackage{xcolor}

begin{document}
begin{tikzpicture}[xscale=1.5, yscale=1.5, join=round, rotate around y=50]

draw [->](0,0,0) -- (3,0,0) node[anchor=west]{$x$};
draw [->, dashed](0,0,0) -- (0,3,0) node[anchor=west]{$y$};
draw [->](0,0,0) -- (0,0,3) node[anchor=west]{$z$};

draw [thick](1, 0, 0)--(0, 1, 0) -- (0, 0, 1)--(1, 0, 0);
fill [blue!50!gray!30] (1, 0, 0)--(0, 1, 0) -- (0, 0, 1)--(1, 0, 0);

node[below] at (1, 0, 0) {$1$};% <--- simplified
node[left]  at (0, 1, 0) {$1$};% <--- simplified
node[below] at (0, 0, 1) {$1$};% <--- simplified

%% since we can now see the y-z axis
fill [blue!50!gray!30] (0, 0, 0) -- (0, 1, 0) -- (0, 0, 1)-- cycle;
draw (0,0,0) -- (0, 1, 0) -- (0,0,1) -- cycle;
end{tikzpicture}%
end{document}