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1% fig-i-32.tex — I.32: triangle angle sum (parallel through apex).
2\begin{figure}[H]
3\centering
4\begin{tikzpicture}[scale=1.2, line cap=round]
5 \coordinate (A) at (-1.5, 0);
6 \coordinate (B) at (2.0, 0);
7 \coordinate (C) at (0.5, 2.4);
8 \coordinate (D) at ($(C)!-1.4!(A)$); % line through C parallel to AB, on left
9 \coordinate (E) at ($(C)!-1.4!(B)$); % line through C parallel to AB, on right
10 % Triangle.
11 \draw[very thick] (A) -- (B) -- (C) -- cycle;
12 % Parallel through C, drawn long.
13 \draw[thin] ($(C)!-0.7!(B)$) -- ($(C)!1.5!(B)$);
14 % Side AB extended beyond B to F to expose exterior angle.
15 \coordinate (F) at ($(A)!1.4!(B)$);
16 \draw[thin] (B) -- (F);
17 % Labels.
18 \node[below left] at (A) {$A$};
19 \node[below right] at (B) {$B$};
20 \node[above] at (C) {$C$};
21 \node[below right] at (F) {$F$};
22 \node[above left] at ($(C)!-0.7!(B)$) {$D$};
23 \node[above right] at ($(C)!1.5!(B)$) {$E$};
24\end{tikzpicture}
25\caption{Proposition I.32. Drawing $DE$ through $C$ parallel to $AB$
26makes $\angle DCA = \angle CAB$ (alternate, I.29) and $\angle ECB =
27\angle ABC$ (alternate, I.29); the straight angle at $C$ then sums
28the three interior angles of $\triangle ABC$ to two right angles.}
29\label{fig:I.32}
30\end{figure}
31
