 Hello and welcome to the session. In this session we will discuss about symmetry. First of all let us see when a plane figure is symmetric. A plane figure is symmetric or we can also say is reflection symmetric if and only if there is a reflecting line such that the figure its image over the reflecting line coincide. And this reflecting line the line of symmetry or we can also say it is the axis of reflection of the figure. Consider this triangle if you fold this triangle along the side a b then we find that the triangle a b c fits exactly over the triangle a b d. So we can say that triangle a b c is symmetrical about the line a b. So in this case this line a b is the axis of symmetry or you can say the line of symmetry. So this a b is a reflecting line such that the figure a b d and its image a b c coincide over the reflecting line a b and hence the triangle a b c is symmetric. A symmetric figure may have more than one line of symmetry. It is obvious that if a figure is symmetric that it has one line of symmetry but a symmetric figure can have more than one line of symmetry also. Whenever a figure has two identical halves like for the figure that is triangle a b c the two identical halves are triangle a b d and triangle a b c. So we can say that each half is the line reflection of the other and this figure that is triangle a b c is actually symmetric. Let us consider some figures and their lines of symmetry. First we have a rectangle. For this rectangle p q r s we have two lines of symmetry x y and a b. So a rectangle has two lines of symmetry. Consider the next figure that is a square. For this square p q r s we have four lines of symmetry a b c d q r s and p r these are the four lines of symmetry. So we can say a square has four lines of symmetry. Next figure that we consider is a circle. For a circle we can say that it is symmetrical about three of its diameters. For this figure we have a b c d e f g h are the diameters of the circle. So the circle is symmetrical about any of these diameters. Next figure that we consider is an equilateral triangle. Let us find out the lines of symmetry for an equilateral triangle. This triangle a b c is an equilateral triangle and we find that there are three lines of symmetry for the equilateral triangle a b c these lines l m n are the lines of symmetry and these are the attitudes of the triangle a b c. So we can say that the equilateral triangle is symmetric about the attitudes of the triangle a b c. Thus equilateral triangle is symmetric about its attitude. Next we consider a rhombus and we find out the lines of symmetry for a rhombus. Consider this rhombus a b c d so this rhombus has lines of symmetry and these lines of symmetry are along its diagonals. In this way we can find out the lines of symmetry for any geometric figure. Next we discuss point symmetry a plane figure is said to have point symmetry every line segment of the figure passing through a particular point is bisected by that point and this point is called the center of symmetry. Consider this parallelogram a b c d in which the diagonals a c b d and the line segments e f g h passes through the point o. So the line segments a c b d e f g h passes through the point o and also they are bisected by the point o. So we can say that every line segment of the parallelogram a b c d is bisected by the point o. Hence we can say this parallelogram a b c d has a point symmetry the point o which is the point of intersection of the diagonals of parallelogram a b c d is the center of symmetry. Now as the parallelogram has a point symmetry so we can say the other parallelograms like the rectangles square rhombus will also have point symmetry. Now we can find out whether the geometrical figure has a point symmetry in the same way. Next let's discuss about the symmetry of letters. Consider this letter a of English alphabet. Now let's see if it is symmetrical or not. This letter a is symmetrical about this dotted line that is this dotted line or you can say the axis of symmetry divides this letter a into two identical halves. In the same way for this letter b this dotted line is the line of symmetry since it divides the letter b into two identical halves. In the same way for this letter c this dotted line is the line of symmetry. So these are the letters of the English alphabet which are symmetrical and their lines of symmetry are shown by the dotted lines. So these letters are symmetrical. Let us now see the non-symmetrical letters of English alphabet. These are the letters of English alphabet which are not symmetrical that is they do not have a line of symmetry. Welcome to this session where we have understood the concept of symmetry.