Please read Melody's answer to this person here:
http://web2.0calc.com/questions/investment-3-questions
+129899 Similar because of this logic
OJ / JM = OK / KN
And, by Euclid, whenever a segment drawn in the interior of a triangle divides the sides in the same proportion, that segment is parallel to the base
Thus angle OJK = angle OMN and angle NOM = angle KOJ
So....by AA congruency.....triangle NOM is similar to triangle KOJ
