You can use the xparse package:

\documentclass{article}
\usepackage{tikz,xparse}
\usetikzlibrary{shapes.geometric}

\NewDocumentCommand{\Tri}{m m r()}
 {%
  \node[isosceles triangle, isosceles triangle apex angle=70,
     draw=black,fill=white, inner sep=0pt,anchor=lower
     side,rotate=90,draw=black,
     fill=white, minimum height=#2cm] (#1) at (#3) {};
 }

\NewDocumentCommand\TriTri{mmr(,u)}
 {%
  \Tri{#1}{#2}(#3,#4)
  \Tri{#1}{#2}(#3+2*#2,#4)
  \Tri{#1}{#2}(#3+#2,{sqrt(2*#2*#2)}) %% note #3+#2 = (x1 + x2)/2
                                      %% the sqrt bit is sqrt(size^2 + size^2)
 }

\begin{document}

\begin{tikzpicture}
\TriTri{a}{3}(2,2)
\end{tikzpicture}

\end{document}


The \Tri command accepts three arguments; the first and the second ones are enclosed in braces, while the third is between parentheses, so

\Tri{a}{3}(0,0)


In the body of the definition you'll use (#3) instead of #3, because the parentheses are stripped off.

In the case of \TriTri we have to split off the two coordinates, so we define four arguments; the first and the second ones are enclosed in braces; the third is what goes from ( to a comma, the final one is everything up to ).

Thus I have modified accordingly your code for \TriTri based on the requirements for \Tri.

Tuples in LaTeX
In msh210's answer to this question of mine, he stated that:


  women...who physically could be [intimate with men], which is those who had reached their third birthday.


In comments, he mentioned that:


  age three is the age at which a girl is halachically considered to be physically able to have intercourse.


Could you explain why and where this comes from? Keep in mind I am not Jewish, so if it specific to some non-OT writings, please explain those as well.
