No.
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Not necessarily, except rotational symmetry of order 1.
a right triangle
yes * * * * * Usually, no. Only isosceles right angled triangles have a line of symmetry.
It can have, but only if the two smaller angles are 45 degrees, then there is symmetry about the centre-line.
It can have a line of symmetry but most have none. Not necessarily. In most cases it would have none.