The lines of symmetry are basically the lines which run through a shape thereby that splits shape into two parts and the parts must be identical. The two identical parts are fit perfectly on each other when they are folded and that is one of good thing that it can be folded easily. The identical shape may be considered as asymmetrical figure that has one line symmetry which is necessary.
Normally, a symmetry contains only line of symmetry but it can be one or more lines and it depends on the nature of symmetry. If we fold a shape along its line symmetry then there will be two halves that would be superimposed on each one in a perfect way without creating any kind of disturbance.
There will be more discussion about symmetry and lines of symmetry if you are more interested in knowing all the information related to symmetry and lines of symmetry then you need to read this whole article because here you will get answer of your questions about lines of symmetry.
There is a difference between a simple symmetry and folded symmetry and in this informative article, we will discuss it briefly.
In this article, we will discuss about symmetry and the lines of symmetry along with its types like rectangular symmetry line and rotational symmetry line too. These two types will be discussed in detail so that you can understand all the points related to symmetry and the lines of symmetry. In rectangular symmetry, we will discuss the purpose and the definition also just for you. In this type, there is at least one line of symmetry which is required for the shape to be identified easily without any disturbance.
Another type of symmetry will also be explained in this section named symmetry line of a square. How many lines of symmetry in rectangular symmetry, rotational symmetry and the line of symmetry of square will be mentioned here in order to clear your confusion about these three types of symmetry.
What is a line of symmetry?
In mathematics, something is said to be symmetrical if it can be divided into two equal parts. The line that divides the object into its equal parts is called the line symmetry.
The number of lines of symmetry in a figure
A line of symmetry creates similarity. A shape or structure of an object may have multiple lines of symmetry. Shapes with a line symmetry have only one line that divides them into equal parts.
Symmetric and asymmetric data
A shape or figure that can be divided into two equal parts by a line is called a SYMMETRIC figure. Those shapes and objects which are irregular and do not resemble each other when divided into two parts are called ASYMMETRIC.
Visualizing Lines of Symmetry
Are you interested in visualizing the lines of symmetry? If you want to visualize the lines of symmetry then you should take a piece of paper and then cut it in a shape.
Visualizing the lines of symmetry can be in any shape and the paper that you cut it in a shape will help you to try experiment on it. After visualizing and taking a paper for doing an experiment then you need to fold the piece of paper that you have taken along the possible lines of symmetry.
If the two sides of a paper sit in a perfect way on each other then you have got your line of symmetry. Except this, we will discuss in detail about rectangular line of symmetry and rotational line of symmetry too.
You will get information about these two kinds so that you can clear your points related to these two lines of symmetry.
Symmetry in real life.
Symmetry was taught to humans by nature itself. Many flowers and most animals are harmonious in nature. Inspired by this, humans learned to build their architecture with symmetrical aspects that made buildings balanced and proportionate at their base, like the pyramids of Egypt! We can see Symmetry around us in many forms:
Trees reflected in the crystal clear water and towering mountains reflected in the lake. Peacock feathers and the wings of butterflies and dragonflies have the same left and right sides. Honey bee hives are hexagonal in shape which is symmetrical in nature.
Types of Line of Symmetry
There are three types of symmetry that we are going to discuss in this section in detail and their definition and their purpose will also be explained in order to clear all the points of a reader. We provide an interesting and informative material to our readers so that they can easily get the idea while reading their favorite articles.
Here we will repeat our same strategy that we will describe symmetry, line symmetry and different types of symmetry and in different types of symmetry, we have line symmetry of a rectangle, rotational symmetry and the last one is square symmetry.
There are three types of lines of symmetry which are as under:
- Vertical line of symmetry
- Horizontal line of symmetry
- Diagonal line of symmetry
Vertical line of symmetry
A vertical line that divides an object into two equal parts is called a vertical line of symmetry. This means that a vertical line goes through an object from top to bottom or vice versa and divides it into its mirror parts.
Horizontal line of symmetry
When a horizontal line divides an object into two equal parts, it is called a horizontal line of symmetry. This means that the horizontal line symmetry goes from left to right (or vice versa) in an object.
Diagonal line of symmetry
When a rectangular diagonal / diagonal line divides an object into two equal parts, it is called a diagonal line of symmetry.
Line of Symmetry of Rectangle
There are two lines of symmetry in this type and the two lines of symmetry are divided into two parts which are called identical parts. The shapes maybe in different types of symmetry such as linear symmetry and mirror symmetry too. Reflection symmetry is also included in the shapes which are types of symmetry and also divided into two identical parts.
These three types are included in shapes and the shape consists of two or more lines of symmetry and if we talk about the symmetry of rectangle then it has one of a quadrilateral. The quadrilateral of a rectangle has two opposite sides and these opposite sides are considered as equally parallelograms. There is an additional detail about it that we have mentioned in the following, you should also read the following informative content.
The opposite sides in a symmetry of rectangle are same and they are parallel to each other, the adjacent sides of a rectangle are at right angles. That is why, it can be easily folded along the length but it can be folded only once along its length. The opposite sides of a rectangle can also be folded only once along its width that is another possibility to fold it. This will give you two lines of symmetry that is our main topic that we are discussing here. A rectangle’s length is longer that the width of a rectangle so when you fold it rectangular diagonal then there are two halves which do not completely overlap and hence we are not able to match the shapes.
The corners of a half right-angled corners that we folded i.e. half of it are resembling a right triangle, are separated from each other and they are misaligned too. The result of this process is that the diagonal is not a symmetry of rectangle and we can say, there are two lines of symmetry in a rectangle symmetry.
A Rotational symmetry of line of a rectangle
When a shape or plane rotates around its axis and remains the same as before, it is called rotational equilibrium. In other words, rotational symmetry exists if the shape remains the same even if it is partially rotated. A rectangle symmetry becomes rotationally symmetric when it is rotated 180° and 360° around its axis. Rotate the rectangle and it will fit the border exactly twice. Once it was 180° and another time it was 360°. For a rectangle, the length is greater than its width, so it can be said that there is no rotational symmetry at 90° and 270°.
Lines of symmetry in a rectangle
In a rectangle symmetry, opposite sides are equal and parallel to each other and adjacent sides are at right angles. Thus, it can be joined along its length, and once along its breadth, giving us two lines of symmetry. Sides will only superimpose when joined along these lines. Two lines of symmetry of a rectangle.
Since the length of a rectangle is always greater than its width, folding along the rectangular diagonal makes two halves. There will not be a perfect superimposition. The right-angled corners of the folded half will be separated from each other, in the wrong order. Thus diagonals are not parallel lines to a rectangle.
Lines of symmetry in a rectangle are the lines that divide the rectangle into two equal parts and there are 2 lines of symmetry in a rectangle. One is drawn horizontally and the other vertically. It should be noted that the diagonals of a rectangle are not considered parallel lines in the rectangle because they do not divide the rectangle symmetry into equal and equal parts.
The Lines of symmetry in a square
So now that we know how many lines of symmetry a rectangle has, let’s take a quick look at another rectangle, the square. For a square, all its sides are equal, opposite sides are parallel to each other and adjacent sides are at 90°.
Thus, in addition to two lines of symmetry like a rectangle, a square also has lines of symmetry along its diagonal. As the diagonal will divide the square into two right-angled isosceles triangles that will sit exactly on top of each other.
Frequently Asked Questions
There are few questions which will help you in understanding the things more clearly:
What is line of symmetry defined?
A line symmetry can be defined as an imaginary line drawn either horizontally or vertically along the center of a figure to divide it into two equal parts.
How to find lines of symmetry in a shape?
When a figure is folded and if one half is equal in size to the other half, we say that the fold line is a line symmetry. A figure may have more than one line of symmetry.
How do I find lines of symmetry in a rectangle?
When we fold a rectangular piece of paper horizontally or vertically through its middle, we get two equal parts of the figure. Those fold lines are the symmetry lines of a rectangle symmetry.
What is rotational equilibrium?
A shape is said to be rotationally symmetrical if it remains in the same shape as it was before after being rotated through a certain angle.
Does the rectangle have rotational symmetry?
Yes, a rectangle has a rotational symmetry at 180° and 360°.
A Symmetry line runs through a shape which splits in two identical parts which are fit perfectly on each other. The identical parts can be folded and they are considered as asymmetrical figure which has one necessary symmetry line. There are almost three kinds of symmetry line that we already mentioned here, all the kinds contain specific features.
The purpose of all the types of symmetry have been described here i.e. the purpose of vertical, horizontal and also the purpose of rectangular diagonal have been discussed here. You just need to read all the information because all the information is for those who are math lovers.
There is a question in a symmetry that how many lines of symmetry contain, there are two lines of symmetry in a rectangle. In a rectangle symmetry, there are opposite sides which are equal and adjacent at right angle which can be easily folded.