# How many lines of symmetry can a pentagon have?

## How many lines of symmetry can a pentagon have?

5
Pentagon/Line of symmetry

What type of symmetry does a pentagon?

five-fold symmetry
The regular pentagon possesses a five-fold symmetry, that is, a rotational symmetry of order 5, given by rotations in the plane of the polygon about its center of angles 2π/5, 4π/5, 6π/5 and 8π/5. The rotation of 10π/5 = 2π is the identity. It has also five lines of reflection symmetry.

How many axis does a pentagon have?

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon….

Pentagon
Internal angle (degrees) 108° (if equiangular, including regular)

### What shape has no lines of symmetry?

Parallelogram
Parallelogram. A parallelogram has no lines of symmetry. It has rotational symmetry of order two.

What is the least angle of rotation of a pentagon?

This is because the regular pentagon has rotation symmetry, and \begin{align*}72^\circ\end{align*} is the minimum number of degrees you can rotate the pentagon in order to carry it onto itself.

What shape has 2 line of symmetry?

Rectangle
Rectangle. A rectangle has two lines of symmetry. It has rotational symmetry of order two.

#### What is no line of symmetry?

A circle has an infinite number of lines of symmetry since it can be folded about any diameter. Some shapes, such as a scalene triangle, have no lines of symmetry – it is not possible to fold the shape about a line so that the two halves fit exactly on top of one another.

How many axes of symmetry does a pentagon have?

A regular pentagon has five symmetry axes – each one connecting a vertex with the middle of the edge opposite this vertex. A regular pentagon also has rotational symmetry – if you rotate it by any multiple of 72 degrees clockwise or anti-clockwise you get a regular pentagon as well.

Is it possible to have a pentagon with all 5 vertices on the same line?

It is impossible to have a pentagon with all 5 vertices lying on the same line. A line passing through one vertex can certainly work (for regular pentagons, the ” home plate ” shape, etc.). Is it possible that a line passing through 3 vertices of a pentagon to be a line of symmetry?

## Why do crystals not have 5 fold symmetry?

Crystals do appear to have 5-fold symmetry but these symmetries are not possible. Crystals can only exist in the 2, 3, 4 or 6-fold rotational axis. The external shape of a crystal is based on a geometric arrangement of atoms, which explains why crystals only have 2, 3, 4, and 6 folds.

How are lines of symmetry related to each other?

Note that to be a line of symmetry, there should be an equal number of vertices on each side of the line. Consequently, there must be an even number of vertices not lying on the line, so the line must pass through an odd number of vertices.