Class 6 Maths Chapter 9 Extra Questions Symmetry
Class 6 Maths Symmetry Extra Questions
NCERT Class 6 Maths Chapter 9 Symmetry Extra Questions and Answers
Very Short Answer Type Questions
Question 1.
Find the line of symmetry in the following figure.
Answer:
In the given figure, the line of symmetry will be
Question 2.
Draw the maximum number of lines of symmetry ¡n an equilateral triangle.
Answer:
The maximum number of lines of symmetry in an equilateral triangle will be 3 as shown below
Question 3.
Draw the mirror image of English letter E, when mirror is placed on the right side.
Answer:
The mirror image of English letter E will be
Question 4.
Draw the mirror image of the following figure.
Answer:
The mirror image of given figure will be
Question 5.
Copy the image and draw the corresponding mirror image of it.
Answer:
The mirror image will be
Question 6.
List the letters of alphabet having same mirror image, when the mirror is placed on right side.
Answer:
A, H, I, M, O, T, U, V, W, X, Y are the letters, whose mirror images are same.
Question 7.
Determine the final figure obtained from the following Steps.
Answer:
The final figure obtained
Question 8.
Give the order of the rotational symmetry of the given figure.
Answer:
The order of rotational symmetry is 3 having angle of rotation equal to 120°.
Short Answer Type Questions
Question 1.
Draw all lines of symmetry for each of the following figure.
Answer:
Question 2.
Given here is a figure of a few folded sheet and designs drawn about the fold. Draw a rough diagram of the complete figure that would be seen, when the design is cut off.
Answer:
The rough diagram of complete figure would be seen as
Question 3.
Does the following figure have rotational symmetry?
Answer:
No, it does not have a rotational symmetry.
Question 4.
State the order of rotation and angle of rotation of the following figure.
Answer:
The order of rotation is 4 and angle of rotation of given figure is \(\frac{360^{\circ}}{4}\) = 90°
Question 5.
State the order of rotation and angle of rotation of the following figure.
Answer:
The given figure have order of rotation is 3 and angle of rotation will be \(\frac{360^{\circ}}{3}\) = 120°
Question 6.
State the order of rotation and angle of rotation of the following figure.
Answer:
The given figure is a hexagon. So, the order of rotation is 6 and angle of rotation of hexagon is \(\frac{360^{\circ}}{6}\) = 60°
Long Answer Type Questions
Question 1.
The flag of Japan is shown below. How many lines of symmetry does the flag have?
Answer:
The flag of Japan shows line of symmetry as
Hence, two lines of symmetry is shown in flag of Japan.
Question 2.
Draw all the lines of symmetry for the following letters if they exist.
Answer:
Question 3.
Does the figure have rotational symmetry?
Answer:
The given figure does not show rotational symmetry, because one part of design is undarken, whereas other three part are darken. Hence, the design does not show symmetry.
Question 4.
State whether the figure shows rotational symmetry. If yes, then what is the order of rotational symmetry?
Answer:
The given figure shows rotational symmetry. The order of symmetry is 4, which is clear from the following figure :
Note The dot is placed just to identify positions of the figure.
Question 5.
In the following figure, show if possible both line and rotational symmetry.
Answer:
(i) In the given figure, line symmetry will be shown as
Also, rotational symmetry will be shown as
\(\frac{360^{\circ}}{8}\) = 45° i.e. rotational angle is equal to 45°.
(ii) In.the given figure, line symmetry will be shown as
Also, rotational symmetry will be shown as
\(\frac{360^{\circ}}{8}\) = 72° i.e. rotational angle is equal to 72°.
Question 6.
In each of the following figures, write the number of lines of symmetry and order of rotational symmetry.
Answer:
| Figure | Number of lines of symmetry | Order of rotational symmetry |
| i. | 1 | 1 |
| ii. | 1 | 1 |
| iii. | 1 | 1 |
| iv. | 2 | 2 |
| V. | 1 | 1 |
| vi | 0 | 2 |
| vii | 1 | 1 |
| viii | 0 | 3 |
| ix | 4 | 4 |
| X | 1 | 1 |
| xi | 0 | 1 |
| xii | 1 | 1 |
| xiii | 0 | 2 |
| xiv | 0 | 1 |
| XV | 1 | l |
| xvi | 1 | 1 |
| xvii | 2 | 2 |
| xviii | 0 | 1 |
| xix | 3 | 3 |
| XX | 1 | 1 |
| xxi | 1 | 1 |
| xxii | 3 | 3 |
| xxiii | 0 | 2 |
Case-Based Questions
Question 1.
The picture shows a girl and her reflection in a mirror.
(i) Can you draw a line of symmetry on this picture? Mention Yes or No. Justify your choice.
(ii) The girl has her right hand raised. Why does it look like her left hand in the mirror image?
(iii) Points, P, Q, R and S are marked on the girl and their mirror reflections P’, O’ ,R’ and S’are marked on the image. Which point and its image in the mirror have the greatest distance between them?
(a) P and Q
(b) Q and Q’
(c) R and R’
(d) P’ and S’
(iv) Which type of symmetry does the picture show?
(a) Line symmetry
(b) Point symmetry
(c) Rotation symmetry
(d) Reflection symmetry
(v) In the above picture, XYZW is a mirror. Why does it produce a symmetric image? Give your explanation using the points shown in the image.
Answer:
(i) A line of symmetry is the line that divides a shape of an object into equal and symmetrical parts. We call this line axis of symmetry or mirror line because it divides the figure symmetrically and the divided parts look like mirror reflections of each other.
Here, they have already given the reflection and there is no fixed line which divides the figure into two identical parts.
Hence, drawing a line of symmetry is not possible.
(ii) A mirror image (i.e. in a plane mirror) is a reflected duplication of an object that appears almost identical but Is reversed in the direction perpendicular to the mirror surface.
So, in mirror reflection, right-orientation changes to left orientation.
That is why, when the girl has her right hand raised, it looks like her left hand in the mirror image.
(iii) (c) We have to find the longest distance of points given i.e. P, Q, R, S and P’ ,Q’ ,R’ and S’.
P is the real image and P’ is the image in the mirror reflection.
Since, we know that a mirror image is a reflected duplication of an object that appears almost identical but in reversed in the direction perpendicular to the mirror surface.
We can see that in figure, the distance between R and R’ is the longest or the greatest.
(iv) (d) The given image is same as image in mirror, so the symmetry is reflection symmetry.
Hence, the required answer is reflection symmetry.
(v) XYZW produce a symmetric image in the mirror due to the point symmetry.
Point symmetry is said to occur when two in the cartesian system lie at the same distance from the coordinate axis but in an opposite direction.
H In the given figure the mirror produce point symmetry across its plane.
Hence, the required answer is obtained.
Question 2.
A quadrilateral is drawn on a square grid. 0 is the dot marked on one vertex’of the quadrilateral.
(i) How many lines of symmetry are there in this quadrilateral?
(a) 0
(b) 1
(c) 2
(d)4
(ii) Draw three more congruent quadrilaterals around 0 so that the complete figure has rotational symmetry of order four.
(iii) Which of the following statements about a parallelogram’s symmetry is true?
(a) A parallelogram has neither a line of symmetry nor rotational symmetry.
(b) A parallelogram has a line of symmetry but no rotational symmetry.
(c) A parallelogram has a point symmetry and rotational symmetry but no line of symmetry.
(d) A parallelogram has rotational symmetry but no point or line symmetry.
(iv) Jyoti claims that rotational symmetry of order 1 implies no rotational symmetry. Do you agree or disagree with her claim? Give reasons.
Answer:
(i) (a) A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts and also called as axis of symmetry.
Here, we can see that there are no line of symmetry Hence, the required answer is 0.
(ii) By drawing three more congruent quadrilaterals from the reference point O, the figure will be
So, the complete figure has rotational symmetry of order four.
(iii) (c) A parallelogram has a point of symmetry and rotational symmetry but no line symmetry.
(iv) Agree. If the given angle is a factor of 360°, only then the figure will have rotational symmetry of order more than one.
e.g. 45° is a factor of 360°, so the figure will have rotational symmetry of order more than 1 and there would be 8 rotations.
Hence, every objects looks similar after 360° rotation.
Question 3.
Here is a picture of a car wheel.
What is the order of rotational symmetry for this wheel?
Answer:
Here, in this case there are four positions in which the trim will look exactly the same. These occur when the wheel is rotated through one-fourth of a complete turn, two-fourth and three-fourth of a turn and finally a complete turn (when, of course, the wheel is back in its original position).
Therefore, the order of rotational symmetry of wheel is 4.
Skill Based Questions
Question 1.
Manya writes first letter of her name on a tracing paper and draws a line Vertically on it at the centre as shown below. She then folds the paper along the line and gets two parts of alphabet M.
(a) Do the two parts Coincide with each other?
(b) Does M have horizontal line of symmetry? if not why?
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.
(iii) Yes
Question 2.
(i) Find out the letters given in the above image having vertical line of symmetry.
(ii) Find out the letter given in the above image having horizontal line of symmetry.
(iii) Draw the mirror image of above image, when mirror is placed on the right side.
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)
