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What does it mean for a shape to not have either rotational and reflectional symmetry?
Wiki User
∙ 9y ago
Simply that it is an asymmetric shape.
Wiki User
∙ 9y ago
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What shape has order of rotational symmetry but no lines of symmetry?
no shape does! * * * * * Not true. A parallelogram has rotational symmetry of order 2, but no lines of symmetry.
Is Reflectional symmetry the quality a design has if it maintains all characteristics when it is rotated about an axis lying in its plane?
No, that is false since the question describes rotational symmetry. A reflection of a shape on the Cartesian plane produces a mirror image. A rotation of a shape on the Cartesian plane turns the shape through an angle at a fixed point.
How do you sketch a figure with rotational symmetry but no line symmetry?
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.
What shape has no lines of symmetry and rotational symmetry order 4?
A tetrad has rotational symmetry of order 4. It also has no lines of symmetry. It is also known as a swastica.
A polygon with Rotational symmetry order of 3 is?
A shape like an equilateral triangle would therefore have an order of rotational symmetry of 3
What type of quadrilateral only has rotational symmetry?
A parallelogram has rotational symmetry. A parallelogram does not have reflectional symmetry. The easiest way to do this is to draw a point in the middle of the shape and rotate it to see if the point looks the same from all angles.
Can a shape have rotational symmetry and line symmetry?
Yes. Any equilateral shape can have both rotational and line symmetry.
What shape has order of rotational symmetry but no lines of symmetry?
no shape does! * * * * * Not true. A parallelogram has rotational symmetry of order 2, but no lines of symmetry.
What shape has a rotational symmetry of order 1?
none shapes have 1 rotational symmetry because in rotational symmetry one is none
What shape has a line of symmetry and rotational symmetry?
circle
Which shape line of symmetry but no rotational symmetry?
A semicircle.
Is Reflectional symmetry the quality a design has if it maintains all characteristics when it is rotated about an axis lying in its plane?
No, that is false since the question describes rotational symmetry. A reflection of a shape on the Cartesian plane produces a mirror image. A rotation of a shape on the Cartesian plane turns the shape through an angle at a fixed point.
Does a shape have to be a regular polygon in order to have rotational symmetry?
A line segment would have rotational symmetry.
How do you sketch a figure with rotational symmetry but no line symmetry?
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.
If a shape is a regular pentagon with five sides what must be true?
It has reflectional symmetry It has five lines of symmetry It is symmetrical
What is Rotatioanl symmetry?
Rotational symmetry is the amount of symmetry you would have if you rotated the shape.
Is there a shape that has no line of symmetry but has the rotational symnetry of 4?
The swastika (either the Hindu or, its reverse, the Nazi symbol)
