no.
Pentagon
It has a line of rotational symmetry - along the diagonal.
Axis of symmetry.
yes
Yes
Yes.
No.
yes
Yes * * * * * Not generally.
yes it does.
The lowercase letter "h" does not have a diagonal line of symmetry. It is symmetrical along a vertical line, but not along a diagonal. The shape of "h" is such that if you were to draw a diagonal line through it, the two halves would not mirror each other.
If you draw a diagonal line from corner to corner of a parallelogram, that is a line of symmetry.