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Symmetry Test - 6

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Symmetry Test - 6
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  • Question 1
    1 / -0
    An isosceles triangle has ___________ line(s) of symmetry.
    Solution


    So, there is only one line of symmetry in an isosceles triangle.
  • Question 2
    1 / -0
    After rotating by 90° about the centre, a figure looks exactly the same as its original position. At what other angle will this happen for the same figure?
    Solution
    Rotating by 90° means the figure is rotated by quarter of a turn, i.e. of 360° turn.

    This means the figure will attain its original position after rotating by , , and 1 full turn of 360°; and the respective angles are 90°, 180°, 270° and 360°.

    Therefore, option 4 is correct.
  • Question 3
    1 / -0
    Dheeraj looks at different shapes and notices that they have 4 sides but the order of rotation is 2. Which of the following shapes can make his observation wrong?
    Solution
    A square has 4 sides. Also, its order of rotation is 4.

  • Question 4
    1 / -0
    Which of the following letters has a line of symmetry on both horizontal and vertical axes?
    Solution


    The answer is option 4.
  • Question 5
    1 / -0
    What is the order of rotation of the following figure?

    Solution
    It is an isosceles triangle and has a rotational symmetry of order 1. This means when an isosceles triangle is rotated, it gets its original shape after a complete (360°) rotation.
  • Question 6
    1 / -0
    Which of the following figures does not have a line of symmetry?
    Solution
    There is no line of symmetry in figure of option 2. Rest all figures have at least 1 line of symmetry.
  • Question 7
    1 / -0
    A figure has a rotational symmetry with the angle of rotation of 72°. What can be the order of rotation of that shape?
    Solution
    Order of rotational symmetry =


    So, the order of rotational symmetry of the given shape is 5.
  • Question 8
    1 / -0
    The order of rotation for a star fish is 2 + m. What is the value of m?
    Solution
    A star fish looks like a star having 5 corners. So, its order of rotation is 5, which can be understood by the following figures.




    In the above figures, the rotation of a star fish in anticlockwise direction is shown. In this, I represents the original position and VI represents the final position after a complete (360°) rotation. Therefore, in a rotation of 360°, the shape of a star fish is repeated 5 times.
    So, order of rotation = 5 = 2 + m
    Or m = 3
  • Question 9
    1 / -0
    Which of the following is the correct symmetrical mirror image of the figure given below?

    Solution


    The above figure is the correct the symmetrical mirror image.
  • Question 10
    1 / -0
    How many of the following letters have no line of symmetry?

    W, X, Y, D, J, K, L, N, P, F, G, A, B, C
    Solution
    Letters having no line of symmetry: J, K, L, N, P, F, G
  • Question 11
    1 / -0
    If a square has a hole close to one of its corners, what will be its order of rotational symmetry?
    Solution
    As there is a hole close to one of the corners of the square, we will get the same figure and the same shape after one complete rotation. Hence, its order of rotational symmetry will be 1. This can be understood by the following figures.

  • Question 12
    1 / -0
    Match the following:

    Column I (Shape) Column II (Lines of Symmetry)
    (P) i 4
    (Q) ii 1
    (R) iii 6
    (S) iv 2
    Solution
    A hexagon has 6 lines of symmetry.
    The 'M' shape has only 1 line of symmetry.
    A rhombus has 2 lines of symmetry.
    A shape of plus (+) has 4 lines of symmetry.
  • Question 13
    1 / -0
    If all the following shapes have rotational symmetry of order more than 1, then which of the following shapes is matched incorrectly with its angle of rotation?
    Solution
    The order of rotational symmetry of square is 4.
    Angle of rotation of square =
    That is, after each rotation of 90°, the shape of square looks the same.
  • Question 14
    1 / -0
    State True or False for the following statements.

    (i) The order of rotational symmetry is the number of times an object looks the same as it did originally when it is rotated through 180°.
    (ii) A rectangle has 4 lines of symmetry.
    (iii) A parallelogram has 2 lines of symmetry and zero order of rotation.
    Solution
    Statement 1: False
    A shape has rotational symmetry of order 1 when it still looks the same after a rotation of 360 degrees.
    Statement 2: False
    A rectangle is a shape with two lines of symmetry.
    Statement 3: False
    A parallelogram has zero lines of symmetry, but the order of rotation is 2.
  • Question 15
    1 / -0
    Choose the option which gives the respective values of A, B, C, D and E in the following table.

    Solution
    A rhombus has 2 axes of symmetry which are along both the diagonals. It has a rotational symmetry of order 2 with 180° as the angle of rotation.
    A square has 4 axes of symmetry, i.e. 2 along diagonals and 2 along sides. It has a rotational symmetry of order 4 with 90° as the angle of rotation.
    For an equilateral triangle, the number of axes of symmetry as well as the order of rotation is 3.
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