For Image 1:
Row 1: 1 under (do not repeat), 3 over, 3 under, 3 over, … (repeat).
Row 2: 3 over, 3 under, 3 over, 3 under, 3 over, … (repeat).
Row 3:2 over (do not repeat), 3 under, 3 over, 3 under, 3 over, … (repeat).
Row 4: 2 under (do not repeat), 3 over, 3 under, 3 over, … (repeat).
Row 5: 3 under, 3 over, 3 under, 3 over, … (repeat).
Row 6:1 over (do not repeat), 3 under, 3 over, 3 under, … (repeat).
For Image 2:
Row 1: 1 under, 3 over, 1 under, 3 over, 1 under, … (repeat).
Row 2: 2 under (do not repeat), 1 over, 3 under, 1 over, 3 under, 1 over, … (repeat).
Row 3: 1 over, 3 under, 1 over, 3 under, 1 over, … (repeat).
Row 4: 2 over (do not repeat), 1 under, 3 over, 1 under, … (repeat).
Row 5: 1 under, 3 over, 1 under, 3 over, 1 under, … (repeat).
Row 6: 2 under (do not repeat), 1 over, 3 under, 1 over, 3 under, … (repeat)
NCERT Textbook Page 93
Let Us Try
Draw the following pattern on a grid paper. Part of it is done for you.
Now, complete the rest of the grid to get the full design.
Solution:
Do it yourself.
NCERT Textbook Pages 94-99
Find Out
Can five squares fit together around a point without any gaps or overlaps? Why or why not?
Solution:
No, five square cannot fit together perfectly around a point without any gaps or overlaps. Because, each angle of a square is a right angle. For shapes to fit perfectly around a point without gaps or overlaps (i.e., to form a tessellation around that point), the sum of the angles of the shapes meeting at that point must exactly equal to 4 right angles.
If we place five squares around a point, the sum of their angles would be 5 right angles which is greater than 4 right angles, so the squares would overlap.
Can regular hexagons (6-sided shapes with equal sides) fit together around a point without any gaps or overlaps? Try and see (a sample hexagon is given at the end of the book). How many fit together at a point?
Solution:
Yes, regular hexagons can fit together around a point without any gaps or overlaps. Three hexagon fit perfectly around one central point, like pieces of a puzzle. They touch each other neatly without any empty spaces in between, and they don’t pile up on top of each other.
What shapes have been used in this pattern?
Solution:
Equilateral triangles, Regular hexagons used in the above pattern.
Continue the pattern given below and colour it appropriately.
Solution:
Do it yourself.
Do regular octagons fit together without any gaps or overlaps?
Solution:
No, regular octagons do not fit together perfectly without any gaps or overlaps to form a tessellation.
Look at the pattern given below. What shapes are coming together at the marked points? Are the same set of shapes coming together at these points? Continue the pattern and colour it appropriately.
Solution:
Shapes coming together at the marked points are square. Yes, same set of shapes are coming together at these points.
Here is a tiling pattern made using two different shapes-squares and triangles. Are the triangles equilateral? Why or why not?
Solution:
Yes, as the sides of a square are equal, so the sides of triangles used to fill the gap must be of equal sides. So, the triangles are equilateral.
What geometrical shapes can you make by fitting 2 of these triangles together? Trace the shapes you created.
Solution:
Do it yourself.