Practicing with Maths Mela Class 5 Solutions Chapter 10 Symmetrical Designs Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 5 Maths Chapter 10 Symmetrical Designs Question Answer Solutions
Symmetrical Designs Class 5 Maths Solutions
Class 5 Maths Chapter 10 Solutions
(NCERT Pg 136)
Question 1.
Which of the following alphabet cutouts can be made by just drawing half (\(\frac{1}{2}\)) or quarter (\(\frac{1}{4}\)) of the letter? You can do it by drawing lines of symmetry on the letters.
(i) Which of the letters have a horizontal line of symmetry?
(ii) Which of the letters have a vertical line of symmetry?
(iii) Which letters have both vertical and horizontal lines of symmetry?
Answer:
The alphabets made by just drawing half or quarter of the letter are
(i) The letters with a horizontal line of symmetry are E, X, K and O.
(ii) The letters with a vertical line of symmetry are X, T, V, and O.
(iii) The letters with both vertical and horizontal lines of symmetry are X and O.
Let Us Do (NCERT Pg 136)
Question 2.
Use lines of symmetry of make paper cutouts of diya, boat, and other designs. Looks along the border to the page of find the pictures.
Answer:
Let Us Make a Windmill Firki (NCERT Pg 137-138)
Question 3.
Observe the dot in the firki. Does the firki look the same after \(\frac{1}{4}\), \(\frac{1}{2}\), \(\frac{3}{4}\), and a full turn?
Answer:
Yes, the firki looks the same after \(\frac{1}{4}\), \(\frac{1}{2}\), \(\frac{3}{4}\) and full turns.
Question 4.
Observe the letters below. Do they look the same when turned? Dots have been marked on the letters to keep track of the orientation of letters. You may also cut out the letters and fix the centre point of the letter by a nail or use a tracing paper to check if the letter looks the same when turned.
Answer:
Let Us Do (NCERT Pg 138)
Question 5.
(i) Find symmetry in the digits.
(a) Which digit(s) have reflection symmetry?
(b) Which digit(s) have rotational symmetry?
(c) Which digit(s) have both rotational and reflection symmetries?
(ii) (a) Now, let us look at the following numbers: II, 1001
Do these have rotational symmetry, reflection symmetry or both symmetries?
(b) Give examples of 2-, 3- and 4-digit numbers which have rotational symmetry, reflection symmetry, or both.
Answer:
(i) (a) The digit having reflection symmetry are 1,3,8 and 0.
(b) The digit(s) having rotational symmetry are 0,1 and 8.
(c) The digit(s) having both rotational and reflection symmetries are 0,1 and 8.
(ii) (a) Both II and 1001 have reflection and rotational symmetries.
But 1001 has only reflection symmetry.
(b) Rotational symmetry and reflection symmetry
2-digit-88, II
3-digit-808, 101
4-digit-8008, 1001
Making Designs (NCERT Pg 139)
Question 6.
(i) Does the design have rotational symmetry? Yes/No.
(ii) Try to change the design by adding some shape(s) so that the new design looks the same after a \(\frac{1}{2}\) turn. Draw the new design in your notebook.
(iii) Now try to modify or add more shapes so that the new design looks the same after \(\frac{1}{4}\) turn. Draw the new design in your notebook.
(iv) Do the new designs have reflection symmetry? If yes, draw the lines of symmetry.
Answer:
(i) No, the given design does not have rotational symmetry because it looks different after some rotation less than full rotation.
(iv) Yes, the new designs can have reflection symmetry.
The new designs have 2 lines of reflection symmetry each as shown as below.
Let Us Think (NCERT Pg 139)
Question 7.
(i) Does this design look the same after \(\frac{1}{2}\) turn?
(ii) Does the design look the same after \(\frac{1}{4}\) turn?
(iii) Colour the square given in the adjoining figure using two colours so that the design looks the same after every \(\frac{1}{4}\) turn.
(iv) How many times does this shape look the same during a full turn?
(v) Do these designs have reflection symmetry also? Draw the line(s) of symmetry.
Answer:
(i) Yes, the design looks the same after \(\frac{1}{2}\) turn.
(ii) No, the design looks different after \(\frac{1}{4}\) turn.
(iii)
(iv) The square with diagonals looks the same 4 times during a full turn.
(v) Yes, desigr (b) has reflection symmetry.
In figure (i), 2 lines of symmetry.
Let Us Do (NCERT Pg 139-140)
Question 8.
Cut out squares and equilateral triangles with the same side length. These are provided at the end of the book.
Make different symmetrical designs by using these two shapes.
Answer:
Do yourself.
Question 9.
I.
(i) Does this shape have reflection symmetry?
(ii) If yes, draw its lines of symmetry.
(iii) Does it have rotational symmetry?
(iv) If yes, at which turn?
(v) Does it have both symmetries?
II. Now, make your designs. Sort your designs in 3 categories-designs with only rotational symmetry, designs with only reflection symmetry, and designs with both rotational and reflection symmetry.
Answer:
I. (i) Yes, the shape has reflection symmetry.
(ii)
A vertical and a horizontal i.e. 2 lines of symmetry.
(iii) Yes, the shape has rotational symmetry.
(iv) It can be rotated by \(\frac{1}{2}\) turn to appear the same.
(v) Yes, the shape has both reflectional and rotational symmetries.
II. Do yourself.
Let Us Explore (NCERT Pg 140-141)
Question 10.
Below are images of wooden blocks and a part of their prints. Match each block to its correct print by drawing a line. One is done for you.
Answer:
Question 11.
Observe the pattern made by the wooden block below. We get the final print by using the block 4 times.
Answer:
The design B looks the same after every \(\frac{1}{4}\) turn. This design has both reflection and rotational symmetry.
Let Us Do (NCERT Pg 141)
Question 12.
Observe the shapes given on the border. Which of the shapes have reflection symmetry? Put a (✓) mark on them. Put a (*) on the shapes that have rotational symmetry.
Answer:
Here, the shapes having reflection symmetry are (i), (iii), (iv), (v), (vi), (vii), (viii), (ix), (xi), (xii), (xiii), (xiv), (xvii) (xviii) and (xiv). and the shapes having rotation symmetry are
(i), (ii) (iv), (v), (vi), (vii), (viii), (ix), (x), (xi), (xii), (xiii), (xiv), (xvi), (xvii), (xviii).
Project Work (NCERT Pg 141)
Question 13.
Create symmetrical patterns and designs using vegetable blocks. Some are shown below.
Answer:
Do yourself.