Question

What is the order of symmetry of the square? Give the angle of such rotations.

Answer 1

Hint: This question is based on two concepts of symmetry we can say. First is the order of symmetry and the other is the angle of rotation. We first will clear these concepts and then will move towards the answer. Angle of rotation is related to rotational symmetry only.

Complete step-by-step solution:
Let us assume a square ABCD.

Now if we rotate this square by \[{90^ \circ }\] so that we can check the symmetry.

Now in the next rotation we will continue with addition of \[{90^ \circ }\] each time. So that next two rotations will be of \[{270^ \circ }\& {360^ \circ }\].
After one more rotation,

And last we will get the original square as,

This clears that, we get the original figure or shape after four such rotations. Thus the order of symmetry is said to be 4.
The angles of such rotations are \[{90^ \circ },{180^ \circ },{270^ \circ }\& {360^ \circ }\] .

Note: Note that here we are asked to find the angular rotational symmetry. There exists line symmetry also.
This line symmetry is checked across a line such that if the shape is folded along that line we should get the mirror image of the figure on the other side or it should exactly fold on the other half.
So line symmetry is along the line and rotational symmetry is observed or checked by rotating the figure through different angles.