All regular shapes have a line of symmetry. But you can get rid of its line of symmetry by making it irregular (so the angles aren't the same).
A nonrectangular parallelogram has rotational symmetry, but not line symmetry. Additionally, shapes such as the letters S, N, and Z can be rotated to show rotational symmetry, although they do not have line symmetry.
isoceles triangle
Trapezoid, heart, etc.
Yes, they do exist. In fact, there are infinitely many of them.
It depends on what kind of shape you are asking about. A circle has an infinite number of lines of symmetry, all passing through the center. Regular shapes (triangle, square, rectangle, pentagon, etc.) have at least one. Irregular shapes tend to have no line of symmetry.
Shapes do not always have lines of symmetry. For example, if you have an irregular shape, it will not have a line of symmetry. I am quite certain though that all geometric shapes have a line of symmetry.
No. Asymmetric shapes do not have any lines (or planes) of symmetry.
A square has 4 lines of symmetry
You would call the group of shapes which has at least one line of symmetry symmetrical shapes. Stars, circles, and rectangles are considered symmetrical shapes.
A nonrectangular parallelogram has rotational symmetry, but not line symmetry. Additionally, shapes such as the letters S, N, and Z can be rotated to show rotational symmetry, although they do not have line symmetry.
isoceles triangle
square
It all depends what types of shapes, but take for example a circle, it can have multiple lines of symmetry.
There are infinitely many such shapes. To start with, any regular will do.
Triangle, square, circle.
Symmetry is the line in the middle of any object to split it into two equal parts. some objects or shapes don't always have a 'line' of symmetry.
None. A line of symmetry, if it exists, is infinitely long and so a third of the line cannot exist as a separate entity.