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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Now study some patterns made up of shapes.

Stacked Triangles

Stacked Squares

create and solve
A Koch snowflake is a fractal curve
that begins with an equilateral
Koch Snowflake triangle and then replaces
the middle third of every
line segment with a pair of
line segments that form an
equilateral bump. Draw two fractal
designs in your notebook.

Practice Time 1D

1. A polygon with eight sides is known as an octagon. What are the names of polygons that
have 9 sides and 10 sides?
2. Copy the pattern given below and extend up to the next three steps.

....................... ....................... .......................
Where do you find such a pattern?
3. Count the vertices of each of the regular polygons. Which number sequence do you get?

4. How many little triangles are there in each shape of the sequence of stacked triangles? Count
the number of stacked triangles in iterations 1 to 5 of the figure given above. Do you see
any pattern?

5. Can you arrange the stacked triangle in other ways? If yes, draw it in your notebook.
6. Draw a diagram using 2, 3, 4 and 5 circles touching each other externally or internally.

7. Why is a honeycomb hexagonal in shape? Try to draw a honeycomb-like pattern using another
polygon. Are you able to make such a shape without any gaps between two consecutive polygons?
8. In the drawing of a snowflake sequence, a line segment is replaced by an equilateral bump.
As the process repeats more and more times, the changes become tinier with smaller line
segments. How many line segments are there in each shape of the Koch snowflake? Obtain
the number sequence and find the relationship between two consecutive numbers.

19 Patterns in Mathematics