Question 13 Marks
Give the order of the rotational symmetry of the given figures about the point marked x.
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Question 23 Marks
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.
(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
View full question & answer→(i) An equilateral triangle has 3 lines of symmetry which are shown by dotted lines
Also, an equilateral triangle has rotational symmetry of order 3 as shown below:
(ii) An isosceles triangle has only one line of symmetry, which is shown below by dotted lines and it has no rotational symmetry of order more than 1.
(iii) A parallelogram has rotational symmetry of order more than 1, but not a line symmetry.
(iv) An isosceles trapezium has a line of symmetry, which is shown by dotted lines, but not a rotational symmetry of order more than 1.
Also, an equilateral triangle has rotational symmetry of order 3 as shown below:
(ii) An isosceles triangle has only one line of symmetry, which is shown below by dotted lines and it has no rotational symmetry of order more than 1.
(iii) A parallelogram has rotational symmetry of order more than 1, but not a line symmetry.
(iv) An isosceles trapezium has a line of symmetry, which is shown by dotted lines, but not a rotational symmetry of order more than 1.
Question 33 Marks
Which of the following figures have rotational symmetry of order more than 1:
Answer
View full question & answer→Figure (i) has rotational symmetry of order 4 about the marked point through an angle of $90^{\circ}$.
Figure (ii) has rotational symmetry of order 3 about the marked point through an angle of $120^{\circ}$.
Figure (iii) has no rotational symmetry about the marked point.
Figure (iv) has rotational symmetry of order 2 about the marked point through an angle of $180^{\circ}$.
Figure (v) has rotational symmetry of order 3 about the marked point through an angle of $120^{\circ}$.
Figure (vi) has rotational symmetry of order 4 about the marked point through an angle of $90^{\circ}$.
Hence, figures (i), (ii), (iii), (iv) and (v) have rotational symmetry of order more than 1.
Figure (ii) has rotational symmetry of order 3 about the marked point through an angle of $120^{\circ}$.
Figure (iii) has no rotational symmetry about the marked point.
Figure (iv) has rotational symmetry of order 2 about the marked point through an angle of $180^{\circ}$.
Figure (v) has rotational symmetry of order 3 about the marked point through an angle of $120^{\circ}$.
Figure (vi) has rotational symmetry of order 4 about the marked point through an angle of $90^{\circ}$.
Hence, figures (i), (ii), (iii), (iv) and (v) have rotational symmetry of order more than 1.
Question 43 Marks
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?
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?
Question 53 Marks
In the following figures, the mirror line (L.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?
Question 63 Marks
Copy the figures with punched holes and find the axes of symmetry for the following:
Answer
View full question & answer→On copying the figures with punched holes, the axis of symmetry corresponding to the punched holes are shown by dotted lines in the figures given below:
Question 73 Marks
Sohan writes '$M$' on a tracing paper and draws a line vertically on it at the centre as shown below. He, then folds the paper along the line and gets two parts of alphabet M.
(i) Do the two parts coincide with each other?
(ii) Does M have horizontal line of symmetry? If not, why?
(iii)
(a) Find out the letters given in the above image having vertical line of symmetry.
(b) Find out the letters given in the above image having horizontal line of symmetry.
(c) Draw the mirror image of above image, when mirror is placed on the right side.
(i) Do the two parts coincide with each other?
(ii) Does M have horizontal line of symmetry? If not, why?
(iii)
(a) Find out the letters given in the above image having vertical line of symmetry.
(b) Find out the letters given in the above image having horizontal line of symmetry.
(c) Draw the mirror image of above image, when mirror is placed on the right side.
Answer
View full question & answer→(i) Yes
(ii) As we know that, "A figure is said to be symmetrical about a line $l$, if it is identical on both sides of $l$."
If we draw a line horizontally on '$M$', the figure will not be identical on both sides. Thus, $M$ does not have horizontal line of symmetry.
(iii) (a) The letters '$I$' and '$H$' having vertical line of symmetry.
(b) The letters '$E$', '$I$' and '$H$' having horizontal line of symmetry.
(c)
(ii) As we know that, "A figure is said to be symmetrical about a line $l$, if it is identical on both sides of $l$."
If we draw a line horizontally on '$M$', the figure will not be identical on both sides. Thus, $M$ does not have horizontal line of symmetry.
(iii) (a) The letters '$I$' and '$H$' having vertical line of symmetry.
(b) The letters '$E$', '$I$' and '$H$' having horizontal line of symmetry.
(c)
Question 83 Marks
Answer
View full question & answer→(i) Clockwise
(ii) As a continuous loop, the recycling logo forms as a figure of triangle.
Since, the angle of rotation of triangle $=120^{\circ}$
Thus, the order of rotation of recycling logo
$=\frac{360^{\circ}}{120^{\circ}}=3$
Hence, Ravi's answer is correct that the order of rotational symmetry of recycling logo is 3.
(iii) Yes
(ii) As a continuous loop, the recycling logo forms as a figure of triangle.
Since, the angle of rotation of triangle $=120^{\circ}$
Thus, the order of rotation of recycling logo
$=\frac{360^{\circ}}{120^{\circ}}=3$
Hence, Ravi's answer is correct that the order of rotational symmetry of recycling logo is 3.
(iii) Yes