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Okay, so the first thing to recognize is that if those two lines are parallel, then the two triangles will be similar.
Cool, so let me walk you through the logic of it.
IF those lines are parallel, then the two triangles are similar. If two triangles are similar, then corresponding sides will be proportional. The 4 long side corresponds to the 10 long side, and the 6 long side corresponds to the 14 long side. Therefore, the sides should be proportional. The proportion we should be able to set up is \[\frac{4}{10} = \frac{6}{14}\] but that proportion is not true =( So we say then that the triangles are NOT similar, which means that the lines are NOT parallel. Tl;dnr: Yes. You are correct.
My pleasure, Lala! =D
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