Proposition: 6.05: Triangles with Proportional Sides are Similar
(Proposition 5 from Book 6 of Euclid's “Elements”)
If two triangles have proportional sides then the triangles will be equiangular, and will have the angles which corresponding sides subtend equal.
 Let $ABC$ and $DEF$ be two triangles having proportional sides, (so that) as $AB$ (is) to $BC$, so $DE$ (is) to $EF$, and as $BC$ (is) to $CA$, so $EF$ (is) to $FD$, and, further, as $BA$ (is) to $AC$, so $ED$ (is) to $DF$.
 I say that triangle $ABC$ is equiangular to triangle $DEF$, and (that the triangles) will have the angles which corresponding sides subtend equal.
 (That is), (angle) $ABC$ (equal) to $DEF$, $BCA$ to $EFD$, and, further, $BAC$ to $EDF$.
Modern Formulation
Similar triangles are equiangular (this is the converse of Prop. 6.04).
Table of Contents
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Definitions: 1
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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