 Hi and welcome to the session. Today we will learn about symmetry. We see many symmetrical things around us in our day-to-day life. For example, leaves of a plant, also architects, designers and many other people make use of the idea of symmetry. So let us see what is line symmetry. A figure has a line symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide. For example, have a look at this figure. Here this line divides the given figure in two parts and if we will fold these two parts of the given figure along with this line then we will find that these two parts coincide. That means this is a symmetrical figure and here this line is known as line of symmetry for the given figure or this is also known as axis of symmetry. Now let's see the lines of symmetry for regular polygons. For this first of all let us recall what are regular polygons. Now we know that a polygon is a closed figure made of several line segments and in a regular polygon all the signs are equal angles equal ratio. Now there is an interesting fact regarding regular polygons that is all regular polygons are symmetrical figures. So now let us see the lines of symmetry for a regular polygon say a square. Let us find out the lines of symmetry for the given square. Here if we fold the given square along with this line then we will find that these two parts of the given square coincide with each other. So that means this is one line of symmetry for the given square. Again if we fold the given square along with this line then these two parts of the given square will coincide with each other. That means this is the second line of symmetry for the given square. This is the third line of symmetry for the square and this is the fourth line of symmetry for this given square. Now can we find any other line of symmetry for this square? No we cannot. So that means there are four lines of symmetry for a square. Also a square has four sides. So that means in a square number of sides is equal to the number of lines of symmetry. Now as we can see that in a equilateral triangle there are three lines of symmetry and also we know that there are three sides in a equilateral triangle. That means number of sides is equal to the number of lines of symmetry for a equilateral triangle also. And in a regular pentagon there are five lines of symmetry. Also there are five sides in a pentagon. So here also number of sides is equal to the number of lines of symmetry. So from this discussion we conclude that in a regular polygon number of lines of symmetry is equal to the number of sides. We can also say that a shape has a line symmetry when one half of it is the mirror image of the other half. So a mirror line will help you to visualize the line of symmetry but you need to take care of the left right changes in the orientation. Now let's move on to rotational symmetry if after a rotation an object looks like exactly the same we say that it has a rotational symmetry. Now when an object rotates its shape and size do not change so the rotation an object about a fixed point and this fixed point is called the center of rotation. The angle of turning during a rotation is called the angle of rotation. Here a full turn means rotation of 360 degrees. So a half turn means a rotation 180 degrees. Similarly a quarter turn means rotation of 90 degrees. And now the number of times a figure looks like exactly the same in one full turn that is a turn of 360 degrees is called order of rotation. Let us take an example of a equilateral triangle. So here we have a equilateral triangle. Let us name this point as A and we will rotate this equilateral triangle about this point say O. So here O is the center of rotation. Let us rotate this triangle by an angle of 120 degrees. So here we have rotated this triangle by an angle of 120 degrees thus the point A is over here now but the triangle looks like exactly same. So let us again rotate the triangle by an angle of 120 degrees. So after this rotation the point A is over here but still the triangle looks like exactly the same. So let us rotate the triangle third time by an angle of 120 degrees. So finally after the third rotation the point A reaches at its original position and still the triangle looks exactly the same. Now here we already know that O is the center of rotation and we have rotated the triangle by an angle of 120 degrees. So 120 degrees is the angle of rotation. In these three turns the triangle has taken a full turn that is a turn of 360 degrees and the triangle looks exactly the same three times. So that means the order of rotation is three. We can also say that the equilateral triangle has a rotational symmetry of order three. Now you must have seen the movement of the hands of a clock. The rotation in that movement is known as clockwise rotation otherwise it is known as anticlockwise rotation. So here for this equilateral triangle the direction of rotation is clockwise. Now every object has a rotational symmetry of order one. It occupies same position for a rotation of 360 degrees that is one full turn or one complete revolution. Thus in this way we can find out all the details about the rotational symmetry of an object. Let's move on to our next topic. Line symmetry and rotational symmetry. Now there are some shapes which have line symmetry and there are some shapes which have rotational symmetry. But there are some shapes which have both line symmetry as well as rotational symmetry. For example a circle it has both line symmetry and rotational symmetry. Suppose we have a circle with center O then every line passing through its center that is the diameter will be a line of symmetry for the given circle. For example all these lines that is the diameters are the lines of symmetry for the given circle. Thus we can say that a circle has unlimited number of lines of symmetry. Also if we rotate a circle through any angle about its center then it will look like exactly the same so that means a circle has rotational symmetry as well. Thus a circle is a perfect example of a shape which has line symmetry as well as rotational symmetry. So in this session we have learnt about symmetry. With this we finish this session. Hope you must have understood all the concepts. Goodbye take care and have a nice day.