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Symmetry Test - 7

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Symmetry Test - 7
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  • Question 1
    1 / -0
    A pentagon has _____ lines of symmetry.
    Solution


    From the figure, it is clear that pentagon has 5 lines of symmetry.
  • Question 2
    1 / -0
    After rotating a certain figure at 180°, it looks exactly the same as original position. At what other angle should it be rotated so that it exactly looks the same?
    Solution

    Next angle = 180° + 180° = 360°
  • Question 3
    1 / -0
    Which of the following polygons has both line and rotational symmetries of order 6?
    Solution
    The lines of symmetry in a regular hexagon are as follows:



    The order of rotational symmetry is as follows:

  • Question 4
    1 / -0
    Which of the following letters has 2 lines of symmetry and rotational symmetry of order 2?
    Solution
    Letter A has 1 line of symmetry and rotational symmetry of order 1.
    Letter N has no line of symmetry but has rotational symmetry of order 2.
    Letter S has no line of symmetry but has rotational symmetry of order 2.
    Letter X has 2 lines of symmetry (both vertical and horizontal) and rotational symmetry of order 2.
    Hence, option 4 is correct.
  • Question 5
    1 / -0
    Which two figures among the following have reflectional symmetry about both horizontal and vertical mirrors?


    Solution
    In the following figures, the dotted line represents the mirror line.

    Figure A:


    Figure A has both horizontal and vertical reflectional symmetry.

    Figure B:

    Figure B has only vertical reflectional symmetry.

    Figure C:

    Figure C has no reflectional symmetry.

    Figure D:

    Figure D has both horizontal and vertical reflectional symmetry.

    Hence, option 4 is correct.
  • Question 6
    1 / -0
    Which of the following figures has exactly 3 lines of symmetry?
    Solution
    The figure given in the first option has exactly 3 lines of symmetry.


    The figure given in the second option has 2 lines of symmetry.
    The figure given in the third option has 5 lines of symmetry.
    The figure given in the fourth option has 6 lines of symmetry.
  • Question 7
    1 / -0
    If a square has holes at two opposite corners, what will be its order of rotational symmetry?
    Solution
    When a square has holes at two opposite corners, then we will get the same figure two times during its rotation.
    Hence, the order of rotational symmetry is 2.

  • Question 8
    1 / -0
    In a figure, the angle of rotational symmetry is 71°. What will be the order of rotational symmetry for the figure?
    Solution
    If the angle or rotational is 71°, then symmetry of order is not possible because 360° is not completely divided by 71°.
  • Question 9
    1 / -0
    How many lines of symmetry does a circle have?
    Solution
    There are many lines of symmetry in a circle because it is a symmetrical figure.
    Any line that passes through the centre of a circle will be a line of symmetry. So, there are an infinite number of lines that can be drawn through the centre of the circle.

    Example: AB, CD, EF, GH, IJ, KL, MN and OP are all lines of symmetry for the given circle. We can have an infinite number of such chords in a circle.

  • Question 10
    1 / -0
    How many of the following letters have rotational symmetry of order more than 1?

    B, G, N P, Q, R, S, Z
    Solution
    An object is said to possess rotational symmetry if, while rotating it through 360 degrees, we obtain the same object at least once in the process.
    The number of times in which the object obtains its initial position is called its order of rotational symmetry.
    Among the given letters, only N, S and Z have rotational symmetry and their orders are as:
    N - 2 (order of rotational symmetry)
    S - 2 (order of rotational symmetry)
    Z - 2 (order of rotational symmetry)
    Hence, option 2 is correct.
  • Question 11
    1 / -0
    How many squares must be shaded in the following figure so that the line PQ becomes the line of symmetry?

    Solution
    Two more squares (A and B) must be shaded so that the line AB becomes the line of symmetry.

  • Question 12
    1 / -0
    Fill in the blanks with the help of the table:

    1) If the angle of rotation is 45°, then the order of rotational symmetry is A .
    2) A/An B triangle has both line and rotational symmetries of order more than 1.
    3) The line of symmetry of a circle is C .

    A B C
    P 8 equilateral diameter
    Q 7 isosceles chord
    R 6 scalene radius
    S 5 acute tangent
    Solution
    1) If the angle of rotation is 45°, then the order of symmetry is possible and would be (360°/45°) = 8 rotations.
    2) An equilateral triangle has both line and rotational symmetries of order more than 1.
    3) The line of symmetry of a circle is diameter.
  • Question 13
    1 / -0
    State true (T) or false (F) for the following statements and mark the correct option using the table given below.

    P) The line of symmetry of an isosceles triangles is its base.
    Q) A parallelogram has two lines of symmetry.
    R) The letter 'S' has no line of symmetry.

    P Q R
    A F T F
    B F T T
    C F F T
    D T T F
    Solution
    1) The line of symmetry of an isosceles triangles is its median or altitude; hence a false statement.
    2) A parallelogram has no lines of symmetry; hence a false statement.
    3) 'S' is not symmetrical, so it has zero lines of symmetry; hence a true statement.
  • Question 14
    1 / -0
    Match the following:

    COLUMN I COLUMN II
    1)
    		 (A) Has 4 as the order of rotational symmetry
    2)
    		 (B) Has only one line of symmetry
    3)
    		 (C) Has the number of lines of symmetry equal to the order of rotational symmetry
    4)
    		(D) Has no line of symmetry
    Solution
    The correct matching is as follows:

    COLUMN I COLUMN II
    1)
    		 (C) Has the number of lines of symmetry equal to the order of rotational symmetry
    2)
    		 (D) Has no line of symmetry
    3)
    		 (B) Has only one line of symmetry
    4)
    		 (A) Has 4 as the order of rotational symmetry

  • Question 15
    1 / -0
    Choose the option that respectively represents P, Q, R and S in the following table:

    Shape Centre of Rotation Order of Rotation Angle of Rotation
    Rhombus P
    Regular hexagon Q
    Circle R S


    Solution
    The second option is correct.
    The complete table is as follows:

    Shape Centre of Rotation Order of Rotation Angle of Rotation
    Rhombus Intersecting point of diagonals 2 180°
    Regular hexagon Intersecting point of diagonals 6 60°
    Circle Centre Infinite At every point
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