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(Chapter – 14) (Symmetry), (Class – VII), , Exercise 14.1, Question 1:, Copy the figures with punched holes and find the axes of symmetry for the following:, , Answer 1:, S.No., , Punched holed figures, , The axes of symmetry, , (a), , (rectangle), (b), , 1
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(c), , (d), , (e), , (f), , (g), , (h), , (i), , (j), , 2
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(k), , (l), , Question 2:, Express the following in exponential form:, , Answer 2:, S.No., , Line(s) of symmetry, , Other holes on figures, , (a), , (b), , (c), , (d), , 3
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(e), , Question 3:, In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted, line. Complete each figure performing reflection in the dotted (mirror) line. (You might, perhaps place a mirror along the dotted line and look into the mirror for the image)., Are you able to recall the name of the figure you complete?, , (a), , (b), , (c), , (d), , (e), , (f), , Answer 3:, S.No., , Question figures, , Complete figures, , Names of the figure, , (a), , Square, , (b), , Triangle, , (c), , Rhombus, , (d), , Circle, , 4
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(e), , Pentagon, , (f), , Octagon, , Question 4:, The following figures have more than one line of symmetry. Such figures are said to have, multiple lines of symmetry:, , Identify multiple lines of symmetry, if any, in each of the following figures:, , 5
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Answer 4:, S.No., , Problem Figures, , Lines of symmetry, , (a), , (b), , (c), , (d), , (e), , (f), , (g), , 6
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(h), , Question 5:, Copy the figure given here:, Take any one diagonal as a line of symmetry and shade a few more squares to make the, figure symmetric about a diagonal. Is there more than one way to do that? Will the figure, be symmetric about both the diagonals?, , Answer 5:, Answer figures are:, , Yes, there is more than one way., Yes, this figure will be symmetric about both the diagonals., , 7
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Question 6:, Copy the diagram and complete each shape to be symmetric about the mirror line(s):, , (a), , (b), , (c), , Answer 6:, , 8, , (d)
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Question 7:, State the number of lines of symmetry for the following figures:, (a) An equilateral triangle, (b) An isosceles triangle, (c) A scalene triangle, (d) A square, (e) A rectangle, (f) A rhombus, (g) A parallelogram, (h) A quadrilateral, (i) A regular hexagon, (j) A circle, , Answer 7:, S.No., , Figure’s name, , Diagram with, symmetry, , Number of lines, , (a), , Equilateral triangle, , 3, , (b), , Isosceles triangle, , 1, , (c), , Scalene triangle, , 0, , (d), , Square, , 4, , (e), , Rectangle, , 2, , (f), , Rhombus, , 2, , (g), , Parallelogram, , 0, , 9
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(h), , Quadrilateral, , 0, , (i), , Regular Hexagon, , 6, , (j), , Circle, , Infinite, , Question 8:, What letters of the English alphabet have reflectional symmetry (i.e., symmetry related, to mirror reflection) about., (a) a vertical mirror, (b) a horizontal mirror, (c) both horizontal and vertical mirrors, , Answer 8:, (a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y, mirror, mirror, , (b) Horizontal mirror – B, C, D, E, H, I, O and X, , (c) Both horizontal and vertical mirror – H, I, O and X, 10
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Question 9:, Give three examples of shapes with no line of symmetry., , Answer 9:, The three examples are:, , Quadrilateral, , Scalene triangle, , Parallelogram, , Question 10:, What other name can you give to the line of symmetry of:, (a) an isosceles triangle?, (b) a circle?, , Answer 10:, (a) The line of symmetry of an isosceles triangle is median or altitude., (b) The line of symmetry of a circle is diameter., , 11
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Exercise 14.2, Question 1:, Which of the following figures have rotational symmetry of order more than 1:, , (a), , (b), , (c), , (d), , (e), , (f), , Answer 1:, , Rotational symmetry of order more than 1 are a , b , d , e and f because in these, figures, a complete turn, more than 1 number of times, an object looks exactly the same., , Question 2:, Give the order the rotational symmetry for each figure:, , (a), , (b), , (e), , (c), , (f), , (g), , (d), , (h), , Answer 2:, S.No., , Problem figures, , Rotational figures, , (a), , Order of rotational, symmetry, , 2, , 1
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(b), , 2, , (c), , 3, , (d), , 4, , (e), , 4, , 2
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(f), , 5, , (g), , 6, , (h), , 3, , 3
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Exercise 14.3, Question 1:, Name any two figures that have both line symmetry and rotational symmetry., , Answer 1:, Circle and Square., , Question 2:, Draw, wherever possible, a rough sketch of:, (i), a triangle with both line and rotational symmetries of order more than 1., (ii), a triangle with only line symmetry and no rotational symmetry of order more, than 1., (iii) a quadrilateral with a rotational symmetry of order more than 1 but not a, line symmetry., (iv) a quadrilateral with line symmetry but not a rotational symmetry of order, more than 1., , Answer 2:, (i), , An equilateral triangle has both line and rotational symmetries of order, more than 1., , Line symmetry:, , Rotational symmetry:, , 1
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(ii), , An isosceles triangle has only one line of symmetry and no rotational, symmetry of order more than 1., , Line symmetry:, , Rotational symmetry:, , (iii), (iv), , It is not possible because order of rotational symmetry is more than 1 of a, figure, most acertain the line of symmetry., A trapezium which has equal non-parallel sides, a quadrilateral with line, symmetry but not a rotational symmetry of order more than 1., , Line symmetry:, , Rotational symmetry:, , 2
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Question 3:, In a figure has two or more lines of symmetry, should it have rotational symmetry of, order more than 1?, , Answer 3:, Yes, because every line through the centre forms a line of symmetry and it has rotational, symmetry around the centre for every angle., , Question 4:, Fill in the blanks:, Shape, , Centre of Rotation, , Order of Rotation, , Angle of Rotation, , Order of Rotation, , Angle of Rotation, , 4, , 90, , 2, , 180, , 2, , 180, , 3, , 120, , 6, , 60, , infinite, , At every point, , 1, , 360, , Square, Rectangle, Rhombus, Equilateral triangle, Regular hexagon, Circle, Semi-circle, , Answer 4:, Shape, , Square, , Centre of Rotation, , Equilateral, triangle, Regular, hexagon, Circle, , Intersecting point of, diagonals., Intersecting point of, diagonals., Intersecting point of, diagonals., Intersecting point of, medians., Intersecting point of, diagonals., Centre, , Semi-circle, , Mid-point of diameter, , Rectangle, Rhombus, , 3
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Question 5:, Name the quadrilateral which has both line and rotational symmetry of order more than, 1., , Answer 5:, Square has both line and rotational symmetry of order more than 1., , Line symmetry:, , Rotational symmetry:, , Question 6:, After rotating by 60 about a centre, a figure looks exactly the same as its original, position. At what other angles will this happen for the figure?, , Answer 6:, Other angles will be 120,180, 240,300,360 ., For 60 rotation:, It will rotate six times., , 4
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For 120 rotation:, It will rotate three times., , For 180 rotation:, It will rotate two times., , For 360 rotation:, It will rotate one time., , 5
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Question 7:, Can we have a rotational symmetry of order more than 1 whose angle of rotation is:, (i) 45, (ii) 17 ?, , Answer 7:, (i), (ii), , If the angle of rotation is 45 , then symmetry of order is possible and, would be 8 rotations., If the angle of rotational is 17 , then symmetry of order is not possible, because 360 is not complete divided by 17 ., , 6
