How Many Lines Of Symmetry

Line of Symmetry is a line that splits a form exactly in half. This indicates that both one-half of the object would perfectly match if yous folded information technology along the line. Similarly, the shape would non change if a mirror were positioned forth the line.

Have you wondered why your mirror reflection appears symmetrical while a few objects do not? Or could you lot guess what the similarity between 2 marine animals – a starfish and an octopus are? If yous guessed they take a symmetrical body, then you are correct. A symmetrical body is an object or matter that can be cut along a detail centrality, producing similar shapes. For example, if a starfish is cut across its limbs, you will go like shapes. Or, if an octopus is cut forth its head, it will likewise produce similar shapes. Or, await at your body in the mirror. Doesn't it expect symmetrical from either side if you depict an imaginary axis forth your face up? Now, permit united states of america understand what a symmetrical body or simply, symmetry means.

Line of Symmetry Definition

A line of symmetry is an imaginary line or centrality which passes through the center of a body or an object. If you fold the body along this axis, you volition get two or more similar figures. This centrality is known equally the axis of symmetry.

The term symmetry comes from a Greek give-and-take 'lord's day + metron', which later transformed into Latin 'symmetria', meaning 'with measure out'. Hence, the term symmetry means the country of having two halves that match each other exactly in size, shape, and other parameters.

As seen in the higher up starfish and octopus instance, you will get like shapes if you lot cut them along their axis of symmetry.

Let united states of america take another case and understand the line of symmetry. If you lot see the figure, a foursquare is made initially. You will get ii similar small rectangles if you fold the square horizontally along the direct line. If you lot further fold the square along the vertical line of symmetry, yous volition become four minor squares. And if you farther fold the foursquare along the diagonal lines of symmetry, you lot will get more triangles. Hence, with every fold along the line of symmetry, you volition get a like shape or object.

This line of symmetry is also known as the mirror line because it presents two reflections of an image with the same dimensions that tin can coincide. Hence, information technology is also called reflection symmetry. An object can have more than than one line of symmetry depending on the object's geometry.

'What is a line of symmetry' has been discussed. Now permit'south come up to how many lines of symmetry are there in a detail object.

Agreement how many lines of symmetry a body has?

Various shapes and figures have different lines of symmetry. Each shape tin either have one, two, 3, or any specific number lines of symmetry. Yet, various shapes take infinite lines of symmetry. A few of the shapes' line of symmetry are discussed below.

Kite

A kite has only one line of symmetry. The shape can be cut just vertically, producing mirror images.

Rectangle

If you wonder how many lines of symmetry a rectangle has, you should know information technology has two lines of symmetry, i.e., 1 horizontally and another vertically.

Equilateral triangle

An equilateral triangle has three lines of symmetry. Unlike other triangles, such as scalene, isosceles, or right-angled, an equilateral triangle is the one that has maximum lines of symmetry. These lines of symmetry pass through the eye of the shape and the mid-manner of its sides towards the corners, as shown in the figure.

Circle

A circle has infinite lines of symmetry. Since the shape is symmetrical along all its infinite axes; hence, it has space lines of symmetry.

No lines of symmetry

Various objects exercise non take any lines of symmetry. These objects are known to have zero lines of symmetry. This is due to the fact that they exercise not accept any symmetrical axes. The given shapes below do not have any axis of symmetry.

The indicate to be noted here is that though these objects practice not have any line of symmetry, every bit tin can exist seen in the figure, they will somehow exist similar. If yous see these figures in 2D, they will await asymmetrical. However, if you view these shapes in 3D, like a real key, and meet them from the top, they will accept one line of symmetry and their thickness.

Hence, every 3D body volition have at least ane line of symmetry if its thickness is the same along its length. If the thickness is not like, the objects will non have any line of symmetry.

Now, coming to how to determine which line of symmetry is which, permit's expect beneath!

Types of Line of Symmetry

In that location are diverse types line of symmetry. The main ones are:

Translation symmetry

If the object has symmetry along its forwards and astern paths, it is said to have translation symmetry. In simpler terms, if an object tin can slide symmetrically, then it is translation symmetry. As you can run into in the figure, the epitome has translation symmetry every bit it slides from one position to another.

Rotational symmetry

If the object's shape remains the same when rotated about an axis, so that object is said to take rotational symmetry. The rotation can occur along any centrality. However, the result after rotation must have the same epitome equally before rotation. For instance, see the image below. The image shows rotational symmetry nearly the center centrality that comes out of the paper.

Reflection symmetry

When cut through an axis, the object with mirror images is known to have reflection symmetry. For instance, a butterfly. Information technology has perfect reflection symmetry. One side of the paradigm can overlap or coincide with the other side in this symmetry.

Glide symmetry

The combination of both reflection and translation symmetry is known as glide reflection. It is commutative in nature. This means that if you modify the order of the combination, it volition not change the output of the glide reflection. The perfect example of a glide symmetry is the orientation of leaves on a branch. Not all the orientations of leaves are glide symmetric; withal, the one shown in the figure has glide symmetry. If you rotate the branch, the leaves will movement and come up back to their original shape equally they were before. That's the property of glide symmetry.

Properties of Line of Symmetry

Below are a few properties that you must remember to grasp the concept of line of symmetry finer:

If a body has no line of symmetry, then that implies the effigy is asymmetrical.
A shape or object can have Space lines of symmetry. For instance, in circles.
An object can have ane line of symmetry simply. For example, a butterfly is symmetrical along the y-axis only, having only i line of symmetry.
A few objects can have 2 lines of symmetry just. For instance, the shape shown in the image below:

Some bodies practice have multiple (more than two) lines of symmetry. For case, the shape given below.

Facts About Line of Symmetry

Here are a few facts nigh line of symmetry that will help you memorize the concept ameliorate:

A triangle volition have 3, i or no line of symmetry.
A quadrilateral will have four or two or even no lines of symmetry.
A regular pentagon has v lines of symmetry.
A hexagon has half-dozen lines of symmetry.
A heptagon has 7 lines of symmetry.
A scalene triangle has no line of symmetry.
An isosceles triangle has only ane line of symmetry.
A rectangle has ii lines of symmetry.
An equilateral triangle has 3 lines of symmetry.
A circle has an infinite number of lines of symmetry.

Example 1: Identify how many lines of symmetry does the given effigy have?

Solution: Every bit you tin see from the figure in a higher place, the image looks symmetrical from the left and right sides. If y'all overlap the left and right images, they will coincide perfectly. Hence, the above figure has only one line of symmetry, i.e., the vertical line passing through the middle, cutting the image into two halves.

Example ii: Place how many lines of symmetry exercise the given images have?

Solution: To find the lines of symmetry in the given shapes, permit us study them i at a time.

The first paradigm has only one line of symmetry along the vertical axis.
The second epitome has 2 lines of symmetry, i.e., one horizontally and another vertically.
The tertiary prototype also has only one line of symmetry forth the vertical axis.

Example 3: How many lines of symmetry do the given effigy have?

Solution: The given image has just one line of symmetry. That line of symmetry is glide symmetry. If you cutting the image horizontally and rotate it, then the image will look like to what information technology was earlier. Hence, information technology only has 1 line of symmetry.

Frequently Asked Questions

Q.one How many lines of symmetry tin can an object have at once?

Unlike objects can have different lines of symmetry. For case:

An isosceles triangle has only 1 line of symmetry.
A rectangle has two lines of symmetry.
An equilateral triangle has iii lines of symmetry.
A circle has an infinite number of lines of symmetry.

Q.2 How do you locate a shape's line of symmetry?

To locate a shape's line of symmetry, we can fold the shape in such a way that one half is similar to the other half. The line along which nosotros have folded is known as line of symmetry.

Q.3 How many symmetry lines does a regular polygon possess?

A regular polygon possess 4 lines of symmetry.