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When a shape is rotated about its centre, if it comes to rest in a position and looks exactly like the original, then it has rotational symmetry.
A shape like an equilateral triangle would therefore have an order of rotational symmetry of 3. The general rule for a regular polygon (shapes such as pentagons, heptagons, octagons etc. is, that the number of sides is the same as the number of lines of symmetry, which is also the same as the
rotational symmetry order). This means that a regular hexagon has 6 sides, 6 lines of symmetry and an order of rotational symmetry of 6.
Following from this, then a square, which is a regular polygon, has 4 sides, 4 lines of symmetry and an order of rotational symmetry of 4.
If a shape has rotational symmetry, it must have either line symmetry or point symmetry or both. For example, a five pointed star has 5 lines of symmetry and rotational symmetry of order 5, but does not have point symmetry. A parallelogram has no line of symmetry, but has rotational symmetry of order 2 and also point symmetry.
Only a shape which has line symmetry or point symmetry can have rotational symmetry. When there is point symmetry and also rotational symmetry, the order of the latter is even. For example, the letter 'S' has rotational symmetry of order 2, the regular hexagon of order 6.
On this basis, we would suggest that the letter 'F' does not have a rotational symmetry order as it does not have either line symmetry or point symmetry. It doesn't have a centre around which you could rotate it. Sounds weird, but given the definitions, we think this is the case.
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If a figure has rotational symmetry does it have line symmetry?
yes
Can a figure have line symmetry and not rotational symmetry?
Yes. An ellipse (oval) has two lines of symmetry, but not a rotational symmetry. A parabola has one line and no rotation.
Does z have rotational symmetry but no line symmetry?
The letters H and Z have both line symmetry and rotational symmetry
What does f have rotational symmetry or line symmetry or both or neither?
F has no symetry : line or rotational symmetry
Does a triangle have a line symmetry rotational symmetry or both?
An equilateral triangle has both line symmetry and rotational symmetry. A non-equilateral isosceles triangle has line symmetry but not rotational symmetry. A scalene triangle has neither kind of symmetry.
