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Yes. Always
The sides of the triangle will always meet at angles such that two of them will appear 'diagonal'. But these are not defined as diagonal lines. There are actually no diagonals intersecting any triangle. Try drawing one and connecting the vertices - it doesn't work and you simply end up tracing over the lines that define the triangle.
yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
There are no parallel lines in a triangle !
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.