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What is symmetry?
If a shape or an object can be divided into two equal parts, such that the parts are mirror images of each other, then we can say that the shape possesses a line of symmetry or that the shape or object is symmetrical. The two parts that are obtained by folding the shape along an imaginary line called the line of symmetry.
Here we can observe an example of the line of symmetry.
The triangular shape in the image is divided into two equal parts that are mirror images of each other along the line of symmetry.
Solved Examples
Example 1: Find the line of symmetry for the following shapes.
Solution:
Draw an imaginary line through each shape such that the shapes are divided into two equal parts.
As you can see, the lines of symmetry perfectly divides each shape into two equal parts which are mirror images of each other.
Example 2: Which of the following shapes are symmetric?
Solution:
Let us consider the first shape.
Draw the line of symmetry.
A line of symmetry for the second shape is not possible as we cannot divide it into equal or proportionate and balanced parts.
The line of symmetry for the third shape will be,
Hence, the first and the third shapes are symmetrical.
Example 3: Find the other part of the following shape which comes with a line of symmetry.
Solution:
The line of symmetry divides the shape into two equal parts which are mirror images of each other. We have one part, so the second part will be its mirror image.
So, the other part of this shape will be as shown in the image.
Yes, a triangle can have a line of symmetry and this line divides the triangle into two equal parts.
The two parts will coincide with each other when there is a line of symmetry through them.
The line of symmetry for a polygon shows the parts folded along the line fitting perfectly, while the edges are overlapping each other.
Yes, a rectangle can have more than one line of symmetry, horizontally and vertically.