Q: Which shape line of symmetry but no rotational symmetry?

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

A line segment would have rotational symmetry.

The letters S, N, Z, for example.

A triangle........I think

Parrallelogram (it has rotational symmetry but no lines of symmetry)

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

circle

A line segment would have rotational symmetry.

Yes, it is possible to have a shape that has a line of symmetry but does not have rotational symmetry. An example is the letter "K", which has a vertical line of symmetry but cannot be rotated to match its original orientation.

How about an isosceles trapezoid

The letters S, N, Z, for example.

A triangle........I think

Parrallelogram (it has rotational symmetry but no lines of symmetry)

A shape does NOT need to have line symmetry in order to have rotational symmetry.For example, the letters N, Z and S can be rotated 180° to show symmetry, but none of these show line symmetry.When the folded part Line of Symmetry. Here I have folded a rectangle one way, and it didn't work.

The letters H and Z have both line symmetry and rotational symmetry

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