Question

What is the minimum number of lines of symmetry possible for a general quadrilateral?

Answer 1

Hint: In this question we have to find the lines of symmetry of the general quadrilateral. We have to first line the symmetry. The line of symmetry of a figure means the line about which one part of the figure is a mirror image of the other part. So we have to check which quadrilateral has how many lines of symmetry, since a general quadrilateral means all different types of quadrilaterals.

Complete answer: We should first understand what a quadrilateral is.
A quadrilateral is a polygon that has four edges and four vertices. It has four angles. WE know that there are many types of quadrilaterals. Such as Rectangle, Square. Rhombus and so on.
All of these lines have different lines of symmetry.
We know that a square is a quadrilateral with all sides equal. So let us draw the lines of symmetry of the square.

We can see that the lines of symmetry of a square is $4$ .
Here the diagonals of a square also act as lines of symmetry.
Now we will check for a rectangle. We know that a rectangle is different from a square as it has only opposite sides equal. The diagonals of a rectangle will not act as the lines of symmetry.
Let us see the lines of symmetry of rectangle with diagram:

From the figure we can see that the lines of the symmetry rectangle have: $2$ .
There is another quadrilateral that has no lines of symmetry i.e. Parallelogram.
Parallelogram is a quadrilateral that has opposite sides parallel and equal. No lines of symmetry can be drawn from parallelogram.

In the above figure, the parallelogram has no lines of symmetry.
However it can have a rotational symmetry of order two.
So we can see that there are different types of quadrilaterals that have different lines of symmetry.
So not every line divides a general quadrilateral into symmetrical halves.
Hence there are zero lines of symmetry for the general quadrilateral i.e. $0$.
Therefore, in 6 ways the given three shapes can be arranged in different chains.

Note:
We should note that trapezium is also a type of quadrilateral. We know that a trapezium has one pair of parallel sides. Some trapeziums have one line of symmetry. They are called the isosceles trapezium as they have two equal sides like an isosceles triangle. We can see this through the diagram:

So an isosceles trapezium has lines of symmetry; $1$ .