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A pentagon

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Q: What is a shape with five sides and one line of symmetry?
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What shape has 5 sides and 1 line of symmetry?

polygon!


What shape has 6 sides and 1 line of symmetry?

an irregular hexagon... __/\__ \ / \ / \ /


What shape has 4 sides and 1 line of symmetry?

A kite.


Do polygons have to have one line of symmetry?

The number of lines of symmetry in a polygon corresponds to the number of sides it has. If a polygon has n sides, then its symmetry will be n lines of symmetry and it will have one point of symmetry. A pentagon has five lines of symmetry, nonagon has 9, n-gon has n lines of symmetry, so on and so forth.


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.

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