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MATHS 2 Marks Questions

Symmetry · Gujarat Board (GSEB) STD 7 (GSEB - English Medium). 16 questions.

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2 Marks Questions

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16 questions · timed · auto-graded

Question 12 Marks
Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) $45^{\circ}$ ?
(ii) $17^{\circ}$ ?
Answer
We know that an angle of rotation in one complete turn is $360^{\circ}$. So, if given angle of rotation divides $360^{\circ}$ completely, then for that rotational symmetry of order more than 1 that angle will be possible, otherwise not possible.
(i) Yes, we can have a rotational symmetry of order more than 1 whose angle of rotation is $45^{\circ}$. [$\because 360^{\circ}$ is divisible by $45^{\circ}$ completely]
(ii) No, we cannot have a rotational symmetry of order more than 1 whose angle of rotation is $17^{\circ}$. $\left[\because 360^{\circ}\right.$ is not completely divisible by $\left.17^{\circ}\right]$
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Question 22 Marks
After rotating by $60^{\circ}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Answer
After rotating by $60^{\circ}$ about a centre, a figure looks exactly the same as its original position. This will also happen for the figure at angles $120^{\circ}, 180^{\circ}, 240^{\circ}, 300^{\circ}$ and $360^{\circ}$, respectively.
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Question 32 Marks
Name the quadrilateral which have both line and rotational symmetry of order more than 1.
Answer
The name of quadrilateral having both line of symmetry and rotational symmetry of order more than 1 is square.
Image
It has 4 lines of symmetry and rotational symmetry of order 4.
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Question 52 Marks
(i) In the given figure, can you now tell the order of the rotational symmetry for an equilateral triangle?
Image
(ii) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by $120^{\circ} ?$
Answer
We know that in a complete turn (of $360^{\circ}$), the number of times shape an object looks exactly the same is called the order of rotational symmetry.
(i) It has a rotational symmetry of order 3.
(ii) There are three positions, where the triangle looks exactly the same, when rotated about its centre by $120^{\circ}$.
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Question 62 Marks
What other name can you give to the line of symmetry of
(i) an isosceles triangle?
(ii) a circle?
Answer
Other name of the line of symmetry of
(i) an isosceles triangle is median.
(ii) a circle is diameter.
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Question 72 Marks
Give three examples of shapes with no line of symmetry.
Answer
Three examples of shapes with no line of symmetry are
(i) a scalene triangle
(ii) a parallelogram
(iii) A letter G
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Question 82 Marks
What letters of the English alphabet have reflectional symmetry (l.e. symmetry related to mirror reflection) about
(i) a vertical mirror
(ii) a horizontal mirror
(iii) both horizontal and vertical mirrors
Answer
We know that a shape has reflectional symmetry, if one half of it, is the mirror image of the other half. Letters of the English alphabet having reflectional symmetry about
(i) a vertical mirror are A, H, I, M, O, T, U, V, W, X, Y.
(ii) a horizontal mirror are B , C , D , E , H , I , K , O and X .
(iii) both horizontal and vertical mirrors are H , I , O and X .
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Question 92 Marks
Copy the diagram and complete each shape to be symmetric about the mirror line(s).
Image
Answer
Copying the diagram and then completing all the figures such that each shape is symmetric about the mirror line(s) or line of symmetry, we get the following figures:
Image
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Question 102 Marks
Given the line(s) of symmetry, find the other hole(s).
Image
Answer
With respect to the given line(s) of symmetry, the other hole(s) are marked in the figures given below:
Image
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Question 112 Marks
State whether the figure shows rotational symmetry. If yes, then what is the order of rotational symmetry?
Image
Answer
The given figure shows rotational symmetry. The order of symmetry is 4 , which is clear from the following figure :
Image
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Question 122 Marks
Does the figure have rotational symmetry?
Image
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.
Image
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Question 132 Marks
The flag of Japan is shown below. How many lines of symmetry does the flag have?
Image
Answer
The flag of Japan shows line of symmetry as
Image
Hence, two lines of symmetry is shown in flag of Japan.
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Question 152 Marks
Draw two identical parallelograms, one ABCD on a plece of paper and other $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ on a transparent sheet. Mark the points of intersection of their diagonals $O$ and $O^{\prime}$, respectively.
Place the parallelograms such that $A^{\prime}$ lies on $A, B^{\prime}$ lies on $B$ and so on. $O^{\prime}$ then falls on $O$.
Stick a pin into the shapes at the point $O$.
Now, turn the transparent shape in the clockwise direction.
Image
(i) How many times do the shapes coincide in one full round?
(ii) What is the order of rotational symmetry?
Answer
(i) When we turn the transparent shape in the clockwise direction, we see that there are two such positions.
First, when $A^{\prime}$ is on $A$ and second, when $A^{\prime}$ is on $C$.
This shows that in a full turn (of $360^{\circ}$), the parallelogram has two positions, where it looks exactly the same.
(ii) The parallelogram has rotational symmetry of order 2.
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Question 162 Marks
Which of the following shapes have rotational symmetry about the marked point?
Image
Answer
We know that after a rotation, if an object looks exactly the same as original, then it has a rotational symmetry.
Here, figures (i), (ii), and (iv) have rotational symmetry.
But figure (iii) has no rotational symmetry.
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