Page 1 Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”. These pictures of architectural marvel are beautiful because of their symmetry. Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry (Fig 13.1). We can see that the two halves are mirror images of each other. If we place a mirror on the fold then the image of one side of the picture will fall exactly on the other side of the picture. When it happens, the fold, which is the mirror line, is a line of symmetry (or an axis of symmetry) for the picture. Tajmahal (U.P.) Thiruvannamalai (Tamil Nadu) Fig 13.1 13.1 Introduction Chapter 13 Chapter 13 Chapter 13 Chapter 13 Chapter 13 Symmetry Symmetry Symmetry Symmetry Symmetry 2020-21 Page 2 Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”. These pictures of architectural marvel are beautiful because of their symmetry. Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry (Fig 13.1). We can see that the two halves are mirror images of each other. If we place a mirror on the fold then the image of one side of the picture will fall exactly on the other side of the picture. When it happens, the fold, which is the mirror line, is a line of symmetry (or an axis of symmetry) for the picture. Tajmahal (U.P.) Thiruvannamalai (Tamil Nadu) Fig 13.1 13.1 Introduction Chapter 13 Chapter 13 Chapter 13 Chapter 13 Chapter 13 Symmetry Symmetry Symmetry Symmetry Symmetry 2020-21 MATHEMATICS 262 The shapes you see here are symmetrical. Why? When you fold them along the dotted line, one half of the drawing would fit exactly over the other half. How do you name the dotted line in the figure 13.1? Where will you place the mirror for having the image exactly over the other half of the picture? The adjacent figure 13.2 is not symmetrical. Can you tell ‘why not’? 13.2 Making Symmetric Figures : Ink-blot Devils Take a piece of paper. Fold it in half. Spill a few drops of ink on one half side. Now press the halves together. What do you see? Is the resulting figure symmetric? If yes, where is the line of symmetry? Is there any other line along which it can be folded to produce two identical parts? Try more such patterns. Inked-string patterns Fold a paper in half. On one half-portion, arrange short lengths of string dipped in a variety of coloured inks or paints. Now press the two halves. Study the figure you obtain. Is it symmetric? In how many ways can it be folded to produce two identical halves? List a few objects you find in your class room such as the black board, the table, the wall, the textbook, etc. Which of them are symmetric and which are not? Can you identify the lines of symmetry for those objects which are symmetric? Do This Fig 13.2 You have two set-squares in your ‘mathematical instruments box’. Are they symmetric? 2020-21 Page 3 Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”. These pictures of architectural marvel are beautiful because of their symmetry. Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry (Fig 13.1). We can see that the two halves are mirror images of each other. If we place a mirror on the fold then the image of one side of the picture will fall exactly on the other side of the picture. When it happens, the fold, which is the mirror line, is a line of symmetry (or an axis of symmetry) for the picture. Tajmahal (U.P.) Thiruvannamalai (Tamil Nadu) Fig 13.1 13.1 Introduction Chapter 13 Chapter 13 Chapter 13 Chapter 13 Chapter 13 Symmetry Symmetry Symmetry Symmetry Symmetry 2020-21 MATHEMATICS 262 The shapes you see here are symmetrical. Why? When you fold them along the dotted line, one half of the drawing would fit exactly over the other half. How do you name the dotted line in the figure 13.1? Where will you place the mirror for having the image exactly over the other half of the picture? The adjacent figure 13.2 is not symmetrical. Can you tell ‘why not’? 13.2 Making Symmetric Figures : Ink-blot Devils Take a piece of paper. Fold it in half. Spill a few drops of ink on one half side. Now press the halves together. What do you see? Is the resulting figure symmetric? If yes, where is the line of symmetry? Is there any other line along which it can be folded to produce two identical parts? Try more such patterns. Inked-string patterns Fold a paper in half. On one half-portion, arrange short lengths of string dipped in a variety of coloured inks or paints. Now press the two halves. Study the figure you obtain. Is it symmetric? In how many ways can it be folded to produce two identical halves? List a few objects you find in your class room such as the black board, the table, the wall, the textbook, etc. Which of them are symmetric and which are not? Can you identify the lines of symmetry for those objects which are symmetric? Do This Fig 13.2 You have two set-squares in your ‘mathematical instruments box’. Are they symmetric? 2020-21 SYMMETRY 263 EXERCISE 13.1 1. List any four symmetrical objects from your home or school. 2. For the given figure, which one is the mirror line, l 1 or l 2 ? 3. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well. 4. Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry . (a) (b) (c) (d) (e) (f ) (a) (b) (c) (d) (e) (f) l l 2 l 1 5. In the figure, l is the line of symmetry . Complete the diagram to make it symmetric. 2020-21 Page 4 Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”. These pictures of architectural marvel are beautiful because of their symmetry. Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry (Fig 13.1). We can see that the two halves are mirror images of each other. If we place a mirror on the fold then the image of one side of the picture will fall exactly on the other side of the picture. When it happens, the fold, which is the mirror line, is a line of symmetry (or an axis of symmetry) for the picture. Tajmahal (U.P.) Thiruvannamalai (Tamil Nadu) Fig 13.1 13.1 Introduction Chapter 13 Chapter 13 Chapter 13 Chapter 13 Chapter 13 Symmetry Symmetry Symmetry Symmetry Symmetry 2020-21 MATHEMATICS 262 The shapes you see here are symmetrical. Why? When you fold them along the dotted line, one half of the drawing would fit exactly over the other half. How do you name the dotted line in the figure 13.1? Where will you place the mirror for having the image exactly over the other half of the picture? The adjacent figure 13.2 is not symmetrical. Can you tell ‘why not’? 13.2 Making Symmetric Figures : Ink-blot Devils Take a piece of paper. Fold it in half. Spill a few drops of ink on one half side. Now press the halves together. What do you see? Is the resulting figure symmetric? If yes, where is the line of symmetry? Is there any other line along which it can be folded to produce two identical parts? Try more such patterns. Inked-string patterns Fold a paper in half. On one half-portion, arrange short lengths of string dipped in a variety of coloured inks or paints. Now press the two halves. Study the figure you obtain. Is it symmetric? In how many ways can it be folded to produce two identical halves? List a few objects you find in your class room such as the black board, the table, the wall, the textbook, etc. Which of them are symmetric and which are not? Can you identify the lines of symmetry for those objects which are symmetric? Do This Fig 13.2 You have two set-squares in your ‘mathematical instruments box’. Are they symmetric? 2020-21 SYMMETRY 263 EXERCISE 13.1 1. List any four symmetrical objects from your home or school. 2. For the given figure, which one is the mirror line, l 1 or l 2 ? 3. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well. 4. Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry . (a) (b) (c) (d) (e) (f ) (a) (b) (c) (d) (e) (f) l l 2 l 1 5. In the figure, l is the line of symmetry . Complete the diagram to make it symmetric. 2020-21 MATHEMATICS 264 6. In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric. 13.3 Figures with Two Lines of Symmetry A kite One of the two set-squares in your instrument box has angles of measure 30°, 60°, 90°. Take two such identical set-squares. Place them side by side to form a ‘kite’, like the one shown here. How many lines of symmetry does the shape have? Do you think that some shapes may have more than one line of symmetry? A rectangle Take a rectangular sheet (like a post-card). Fold it once lengthwise so that one half fits exactly over the other half. Is this fold a line of symmetry? Why? Open it up now and again fold on its width in the same way. Is this second fold also a line of symmetry? Why? Do you find that these two lines are the lines of symmetry? A cut out from double fold Take a rectangular piece of paper. Fold it once and then once more. Draw some design as shown. Cut the shape drawn and unfold the shape. (Before unfolding, try to guess the shape you are likely to get). How many lines of symmetry does the shape have which has been cut out? Create more such designs. Do This 1st fold 2nd fold Form as many shapes as you can by combining two or more set squares. Draw them on squared paper and note their lines of symmetry. l 2020-21 Page 5 Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”. These pictures of architectural marvel are beautiful because of their symmetry. Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry (Fig 13.1). We can see that the two halves are mirror images of each other. If we place a mirror on the fold then the image of one side of the picture will fall exactly on the other side of the picture. When it happens, the fold, which is the mirror line, is a line of symmetry (or an axis of symmetry) for the picture. Tajmahal (U.P.) Thiruvannamalai (Tamil Nadu) Fig 13.1 13.1 Introduction Chapter 13 Chapter 13 Chapter 13 Chapter 13 Chapter 13 Symmetry Symmetry Symmetry Symmetry Symmetry 2020-21 MATHEMATICS 262 The shapes you see here are symmetrical. Why? When you fold them along the dotted line, one half of the drawing would fit exactly over the other half. How do you name the dotted line in the figure 13.1? Where will you place the mirror for having the image exactly over the other half of the picture? The adjacent figure 13.2 is not symmetrical. Can you tell ‘why not’? 13.2 Making Symmetric Figures : Ink-blot Devils Take a piece of paper. Fold it in half. Spill a few drops of ink on one half side. Now press the halves together. What do you see? Is the resulting figure symmetric? If yes, where is the line of symmetry? Is there any other line along which it can be folded to produce two identical parts? Try more such patterns. Inked-string patterns Fold a paper in half. On one half-portion, arrange short lengths of string dipped in a variety of coloured inks or paints. Now press the two halves. Study the figure you obtain. Is it symmetric? In how many ways can it be folded to produce two identical halves? List a few objects you find in your class room such as the black board, the table, the wall, the textbook, etc. Which of them are symmetric and which are not? Can you identify the lines of symmetry for those objects which are symmetric? Do This Fig 13.2 You have two set-squares in your ‘mathematical instruments box’. Are they symmetric? 2020-21 SYMMETRY 263 EXERCISE 13.1 1. List any four symmetrical objects from your home or school. 2. For the given figure, which one is the mirror line, l 1 or l 2 ? 3. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well. 4. Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry . (a) (b) (c) (d) (e) (f ) (a) (b) (c) (d) (e) (f) l l 2 l 1 5. In the figure, l is the line of symmetry . Complete the diagram to make it symmetric. 2020-21 MATHEMATICS 264 6. In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric. 13.3 Figures with Two Lines of Symmetry A kite One of the two set-squares in your instrument box has angles of measure 30°, 60°, 90°. Take two such identical set-squares. Place them side by side to form a ‘kite’, like the one shown here. How many lines of symmetry does the shape have? Do you think that some shapes may have more than one line of symmetry? A rectangle Take a rectangular sheet (like a post-card). Fold it once lengthwise so that one half fits exactly over the other half. Is this fold a line of symmetry? Why? Open it up now and again fold on its width in the same way. Is this second fold also a line of symmetry? Why? Do you find that these two lines are the lines of symmetry? A cut out from double fold Take a rectangular piece of paper. Fold it once and then once more. Draw some design as shown. Cut the shape drawn and unfold the shape. (Before unfolding, try to guess the shape you are likely to get). How many lines of symmetry does the shape have which has been cut out? Create more such designs. Do This 1st fold 2nd fold Form as many shapes as you can by combining two or more set squares. Draw them on squared paper and note their lines of symmetry. l 2020-21 SYMMETRY 265 13.4 Figures with Multiple (more than two) Lines of Symmetry Take a square piece of paper. Fold it into half vertically, fold it again into half horizontally. (i.e. you have folded it twice). Now open out the folds and again fold the square into half (for a third time now), but this time along a diagonal, as shown in the figure. Again open it and fold it into half (for the fourth time), but this time along the other diagonal, as shown in the figure. Open out the fold. How many lines of symmetry does the shape have? We can also learn to construct figures with two lines of symmetry starting from a small part as you did in Exercise 13.1, question 4, for figures with one line of symmetry. 1. Let us have a figure as shown alongside. 2. We want to complete it so that we get a figure with two lines of symmetry. Let the two lines of symmetry be L and M. 3. W e draw the part as shown to get a figure having line L as a line of symmetry. 3 lines of symmetry for an equilateral triangle 2020-21Read More

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