Reflection Symmetry and Line of Symmetry
In our day to day lives, we witness numerous objects that have symmetry. An object or a figure is said to be symmetrical if it can be divided into two halves that are exactly equal. The line that divides the object or the figure into two equal halves or congruent halves is called the line of symmetry or the Mirror Line. In reflection symmetry, the first half is a reflection or mirror image of the second half.
- 1. A figure or shape or an object can have one or more than one line of symmetry.
- 2. The direction of the line of symmetry is not fixed.
- 3. Both the halves are congruent and mirror images of each other.
Consider the shape of a heart held vertically. We can divide the heart into two equal halves along the central vertical line. This line is its line of symmetry.
The heart cannot be further folded to get the equal halves. Hence, the heart has only one line of reflection symmetry.
This triangle cannot be divided into equal halves and hence does not have reflection symmetry.
Reflection symmetry can also be illustrated by everyday objects like given below:
Explain how many lines of reflection symmetry do circle, square and an equilateral triangle have?
Problems on Reflection Symmetry:
1. Give four examples of reflection symmetrical objects from your home or at school?
Answer: Refrigerator, Washing Machines, Television Sets, Blackboards.
2. Which is the following two lines dividing the object is the line of reflection symmetry?
Answer: The line l2 is the reflection symmetrical line because it divides the shape or figure into two equal halves. The two halves that we get on division by line l2 are mirror images of each other.
The mirror image will complete the figure as L is the line of symmetry.
4. List the number of lines of symmetry in each of the shape given in the image below:
Answer: (a) There are four lines of symmetry in this figure. (b) There are four lines of symmetry in this figure. (c) There are four lines of symmetry in this figure. (d) There are no lines of symmetry in this figure as the figure does not have any equal sides. (e) There are six lines of symmetry in this figure. (f) There are 6 lines of symmetry in this figure. (g) There are no lines of symmetry in this figure as it is sides are unequal. (h) There are no lines of symmetry in this figure. (i) There are three lines of symmetry in this figure.
5. Can you draw a triangle having only one line of Symmetry?
8. Divide the Alphabets from A to Z on the basis of their line of symmetry that is vertical, horizontal, no line of symmetry and make a list of Lines of symmetry.
Answer: The alphabets A, H, I, M, O, T, U, V, W, X and Y have a vertical line of symmetry. Whereas, the alphabets B, C, D, E, H, I, K, O and X have a horizontal line of symmetry. Some alphabets such as F, G, J, N, P, Q, R, S and Z have zero or no line of symmetry.
9. Show that a human body has reflection symmetry.
Answer: When viewed from the outside, the human body seems to be symmetrical. A vertical axis of symmetry can be drawn through the center of the human body.
Knowledge of reflection symmetry plays an important role in calculation of moment of inertia of objects. This is a very important concept in structural civil designing.