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Symmetry

Reflection

When we speak of reflection the first thing that strikes our minds is a mirror. A reflection is an image that is an exact copy of its original, formed in the mirror. Now, when we see perfectly symmetrical figures, we can easily conclude that both the parts are a perfect reflection of each other.

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Introduction to Linear Symmetry and Line of Symmetry
Introduction to Reflection
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Reflection and Symmetrical Figures

Have you ever noticed why the mirror image of AMBULANCE is written on the medical emergency vehicle, Ambulance? The reason for doing so is that the reflection of word AMBULANCE is seen in the rearview mirror of a vehicle ahead, which helps the driver know that an AMBULANCE is behind them.

Symmetrical Figures

(source: maxpixel)

Seeing yourself in the mirror is the most common thing that we do in a day. In fact, our day starts with looking in the mirror. When you see yourself in the mirror you can see an identical person of same size and shape and face in the mirror. Now, what you see in the mirror is a reflection of yourself and is called the mirror image or reflection image.

An object and its mirror image are perfectly identical to each other. The left and right sides of an object appear inverted in the mirror. This object and its reflection image show mirror symmetry. The mirror line here is the line of symmetry.

So when we see an image of an object in the mirror, then the object is symmetrical with its mirror image. This view is similar to a folded paper. When a paper is folded exactly in the middle, the line of the fold is the line of symmetry.  This line of the fold is like the mirror line. The image formed in the mirror is a reflection of the object in the line of symmetry.

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Reflection of Alphabets and Figures

Now, let’s take the case of a figure or shape or an alphabet. When an alphabet is seen in the mirror we see its exactly inverted reflection. Only alphabets A, H, I, M, O, T, U, V, W, X, and Y are identical reflections of the real image.

When a figure is reflected about the mirror line then the reflection image is congruent to the real image. This means that the lengths and angles of the mirror image are identical to the lengths and angles of the real image. The image, however, is a lateral inversion of the real figure.

So in a nutshell, the reflectional symmetry for symmetrical figures is also referred as a bilateral or mirror symmetry. This occurs when the mirror line works as a line of symmetry that divides a shape into identical halves. Here, each half is a perfect reflection of the other part.

There are some shapes or objects, like circles, squares and triangles, that have more than one line of symmetry. These shapes or objects when seen in a mirror are not lateral inversions of each other, rather are identical reflections.

Solved Examples on Symmetrical Figures

Question 1: The angle between the mirror line and the line segment joining  an image with its point is :

  1. 120°
  2. 90°
  3. 45°

Answer : Option (C). The image formed is parallel to the mirror line while its point is perpendicular to the mirror line.  Hence it is at 9o° to the mirror line.

Question 2: What are the symmetrical figures in math?

Answer: Symmetrical shapes are those figures that have an exact resemblance to its other part when we divide them into two or more equal parts. However, those shapes and figures that do not resemble each other when divided into parts are known as asymmetrical shapes. Furthermore, symmetrical lines can be horizontal, vertical and diagonal.

Question 3: Where is symmetry used?

Answer: We observe symmetry in many places without even noticing it. We can easily notice it in architecture, buildings, arts, designs, etc. Furthermore, natural symmetry makes things more appealing and beautiful. Some examples of natural symmetry are the leaf of plants and trees, flowers, fruits, butterflies, etc.

Question 4: How to know if the figure is symmetrical?

Answer: We can know that a figure is symmetrical or not by splitting it into half. Also, symmetry means that both sides are the exact same when you split them in half. So, if an image looks exactly the same on splitting into half then it is symmetrical.

Question 5: What is asymmetry? Give some examples.

Answer: Asymmetry is just the opposite of symmetry. Asymmetry is when the two or more side of the figure is different in some way. Moreover, these things are crooked and irregular and don’t match perfectly.

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