SSS similarity

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Theorem

$\text{SSS Similarity states that if there are two triangles (shown below), then if }\dfrac{\overline{AB}}{\overline{DE}}=\dfrac{\overline{BC}}{\overline{EF}}=\dfrac{\overline{AC}}{\overline{DF}}\text{, then the two triangles are similar.}$ [asy] pair A,B,C,D,E,F;  A = (4,0);  B = (2,0);  C = (3,1);  D = (6,0);  E = (5,0);  F = (5.5,0.5);  draw(A--B);  draw(B--C);  draw(A--C);  draw(D--E);  draw(E--F);  draw(D--F);  dot("$A$",A,NE);  dot("$B$",B,NW);  dot("$C$",C,N);  dot("$D$",D,NE);  dot("$E$",E,NW);  dot("$F$",F,N); [/asy]