Class 7 Maths Chapter 12 Question Answers - Symmetry

Q1: Write the number of lines of symmetry in each letter  ′ SYMMETRY ′
Ans:
In the word ′SYMMETRY ′  letter  ′R′  and  ′S′  has no line symmetry.
But letter ′Y,M,E,T′ has one line symmetry.

Q2: In the word 'MATHS' which letter shows rotational symmetry of order 2?
Ans:

Observe the letters to determine the required letter.
The given word is ’MATHS’ .
The letters are ’M’, ’A’, ’T’, ’H’ and ’S’ .
If a letter remains the same after a rotation of 180^∘ only, in clockwise or anti-clockwise direction, then the letter has a rotational symmetry of order 2.
Observing the letters of the given word, we can say that, if we rotate the letter ’H’ by 180^∘ in either direction, it will remain the same.
Thus, only ’H’ shows rotational symmetry of order 2.
Hence, the required letter is ’H’.

Q3: Find the number of lines of symmetry of the following shape.
Ans:

There are 4 lines of symmetry for the given figure. The lines of symmetry in the given figure can be represented above.

Q4: Find the number of lines of symmetry of the following shape.
Ans:
There are 4 lines of symmetry for the given figure. The lines of symmetry of the given figure can be represented as follows.

Q5: Find the number of lines of symmetry of the following shape.

Ans:
There is only 1 line of symmetry for the given figure. The lines of The symmetry in the given figure can be represented as above.

Q6: Check whether the given figure is symmetric or not. Draw the line of symmetry as well.

Ans:

Yes, the shape given is symmetric.
The line of symmetry is shown in the above figure.

Q7: 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?
Ans:
Yes there is more than one way
Yes, this figure will be symmetric about both the diagonals

Q8: After rotating by 60^o about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Ans:
Other angles will be 12^o ,180^o ,240^o ,300^o ,360^o

Q9: Which of the above figures have rotational symmetry of order more than 1?
Ans:
Rotational symmetry of order more than 1 is in (a), (b), (d), (e) and (f) because in these figures, in a complete turn for more than 1 number of times, the object would be looking exactly the same.

Q10: Copy the following drawings on squared paper and complete each one of them in such a way that resulting figure has two dotted lines as two lines of symmetry:
Ans:
The given figure can be completed by drawing the same parts as shown in the given figure.
We can draw this by drawing horizontal and vertical line of symmetry
Therefore, the given figure can be completed as follows:

Q11: On a squared paper, sketch the following : A quadrilateral with both horizontal and vertical lines of symmetry.
Ans:
A square is also a quadrilateral and a square has both horizontal and .vertical lines of symmetry. On a squared paper, its figure with both horizontal and vertical lines of symmetry, is given below:

Q12: Find the lines of symmetry for the following shape:
Ans:
The lines of symmetry of the given shape is as follows:
From the above diagram, we observe that line of symmetry is AB.
Hence, the number of lines of symmetry is 1.

Q13: Identify multiple lines of symmetry, if any, in the above figure.
Ans:
If we any of two diagonals of quadrilateral we can see that it cuts image in similar two halves.
With one side is mirror image of other.
So, given figure has two lines of symmetry that are diagonals


Q14: In the following figure if the dotted lines represent the lines of symmetry, find the other hole(s).  
Ans:
As, there is one hole and three axes of symmetry, so there will be three holes on other side with respect to each axes of symmetry.
So, holes will lie on other side of these lines at exact same distance as of first hole.
That is it will be mirror images of first hole with axes of symmetry as mirrors.
So, other holes will lie as shown in figure.
Black hole is mirror image with respect to line 1, red hole is with respect to line 2 and green hole is with respect to line 3 , as shown in figure.

Q15. Mark two points A and B 5.5cm apart. Draw a line PQ so that A and B are symmetric with respect to the line PQ. Give a special name to line PQ.
Ans:
Steps of Construction :
(i) Take point A and B as 5.5cm apart
(ii) Draw perpendicular bisect of the line segment AB
(iii) Now, the perpendicular bisector PQ is the required line of symmetry with respect to points A and B
(iv) Hence, PQ is the perpendicular bisector of AB