Consider the letters of English alphabets, A to Z. List among them the letters which have vertical lines of symmetry (like A).

Consider the letters of English alphabets, A to Z. List among them the letters which have vertical lines of symmetry (like A).

Harshit Singh,
2 years ago

Grade:12th pass

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1 Answers

Pawan Prajapati

askIITians Faculty
60787
Points

2 years ago

Hint:
Here we use the concept of line of symmetry to answer this question. A line of symmetry is said to be a line which cuts a shape exactly in half. We will check all the letters of the English alphabet and find which of the letters have their mirror image along a vertical axis. Then we will list out all those letters.
Complete step by step solution:
In the given problem, we have to find all the letters in the English alphabet which are cut exactly in half by a vertical line. This means that when a vertical line divides the alphabet along the centre, both sides of the alphabet are identical.
Let us consider the alphabet A. We observe that when a vertical line divides it from the centre, the two halves are exactly the same.
In the above figure, we observe that on division of the alphabet A by a vertical line, the half I is the same as half II.
Now, we will consider the alphabet B.
We can see from the above figure that for this alphabet, the two halves are not identical.
The alphabet C does not have vertical symmetry as well. Similarly, the alphabets D, E, F, and G do not have vertical symmetry.
Now, consider the alphabet H. This alphabet has two equal halves as seen in the figure below.
The alphabet I also has vertical symmetry. The alphabets J, K, and L do not have vertical symmetry.
The alphabet M has vertical symmetry but the alphabet N does not have vertical symmetry. The alphabet O is symmetric along a vertical line. The alphabets P, Q, R, and S are not symmetric along a vertical line.
The alphabets T, U, V, W, X and Y also possess vertical symmetry as the line divides then equally in both the parts. However, the alphabet Z does not possess vertical symmetry.
Hence, the alphabets which have vertical lines of symmetry are A, H, I, M, O, T, U, V, W, X and Y.
Note:
There are 3 types of symmetry, namely, vertical, horizontal, and diagonal. To find the line of symmetry, we draw the lines of symmetry to check which one divides the shape into two equal halves. It is not necessary that all shapes are symmetric.
Symmetry is used when doing calculations that involve different shapes like spheres, circles, equilateral or isosceles triangles, etc. For example, suppose I have to make a building. So, if the building is symmetric then my calculation for its analysis is much simpler than if it were not symmetric. This is one example, but in general, symmetry in real life is used to simplify calculations and solve problems more easily.