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Something like the picture below:

Similar triangles sharing a vertex

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Have you drawn atleast one triangle? Then put it in a scope and rotate. You may also use rotate around. – Harish Kumar Aug 2 '14 at 23:51

One option:


% fill the triangle
  (0,0) coordinate (0) -- 
  (4,0) coordinate (1) -- 
  (5,2) coordinate (a) -- cycle;
% draw the marks for the angles
  pic[draw=black,double=gray!30,angle radius=1cm] {angle={1--0--a}}
  pic[draw=black,angle radius=0.5cm] {angle={a--1--0}};
% draw the triangle
  (0) node[below left] {$#1$} -- 
  (1) node[below right] {$#2$} --
  (a) node[right] {$#3$} --
\foreach \Coor in {0,1,a}
  \node[circle,draw,fill=white,inner sep=1.5pt] at (\Coor) {};  




enter image description here

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Here's an approach that doesn't use scoping.








  \coordinate (A) at (0,0);
  \coordinate (B) at (3,1);
  \coordinate (C) at (5,4);

  \draw (A) -- (B) -- (C) -- cycle;

  %% measure of the angle CAB

  %% the length to "AB"

  %% the length to "AC"

  %% scale factor

  \coordinate (B')  at ($(A)+(80:\mydistb)$);
  \coordinate (C')  at ($(A)!\myscalefactor*\mylenAC pt!\anglea:(B')$);

  \draw (A) -- (B') -- (C') -- cycle;



enter image description here

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