No but it does have a perpendicular line of symmetry.
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Not normally but as an isosceles right angle triangle it will have perpendicular lines that meet at 90 degrees.
None but its apex is perpendicular to its base
No but it does have 3 sides 2 of which are of equal lengths.
No
Only one line of symmetry, it is the line that contains the median of the isosceles triangle (that passes through the vertex and perpendicular to the base).