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There are no parallel lines in a triangle !
Not necessarily, as two lines can exist in one plane, but they don't always touch each other. An example would be parallel lines, where the lines are parallel to each other. Lines are also not necessarily straight all the time as it can be curvy too, wherein that a straight line or another curvy line that "does" touch the first curvy line could possibly intersect at more than one point.
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An equilateral triangle contains at least 2 lines of symmetry (it actually contains 3 lines of symmetry). An equilateral triangle is also radially symmetric.If the question is "Is there a triangle with exactly 2 lines lines of symmetry?", the answer is no.
If you mean what type of triangle has perpendicular lines then it is right angle triangle.