Proposition: 6.32: Triangles with Two Sides Parallel and Equal
(Proposition 32 from Book 6 of Euclid's “Elements”)
If two triangles, having two sides proportional to two sides, are placed together at a single angle such that the corresponding sides are also parallel, then the remaining sides of the triangles will be straighton (with respect to one another).
 Let $ABC$ and $DCE$ be two triangles having the two sides $BA$ and $AC$ proportional to the two sides $DC$ and $DE$  so that as $AB$ (is) to $AC$, so $DC$ (is) to $DE$  and (having side) $AB$ parallel to $DC$, and $AC$ to $DE$.
 I say that (side) $BC$ is straighton to $CE$.
Modern Formulation
If in two triangles ($\triangle{ABC},$ $\triangle{DCE}$) two corresponding sides are proportional $$\frac{\overline{AB}}{\overline{AC}}=\frac{\overline{DC}}{\overline{DE}}$$ and the triangles have a common edge ($C$), then the remaining sides ($\overline{BC},$ $\overline{CE}$ are collinear).
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016