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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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Q: How do you sketch a figure with rotational symmetry but no line symmetry?

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yes

z

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.

Yes. An ellipse (oval) has two lines of symmetry, but not a rotational symmetry. A parabola has one line and no rotation.

A circle and square.

Line

Many figures. For example, an ellipse.

You turn it a quarter to see if it still has a line of symmetry.

z has no line of symmetry and it does have rotational symmetry so yes

It has line symmetry (straight down the center) but not rotational symmetry.

A line has rotational symmetry of order 2.

A line has 180 degrees rotational symmetry.

F has no symetry : line or rotational symmetry

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.

Yes. Any equilateral shape can have both rotational and line symmetry.

No A rectangle has rotational symmetry as well

Line symmetry.

A rectangle is a possible candidate, as is an ellipse.

Both.

parallelogram * * * * * A parallelogram does have rotational symmetry (order 2).

Line symmetry = Reflection symmetry. Point symmetry = Rotational symmetry.

Yes, the capital letter N has rotational symmetry but no lines of symmetry:

Only an equilateral triangle has rotational symmetry.

A semicircle.

circle