Exercises (Page 228)
8. Find the lines of symmetry for the kolam below.
The Kolam is a star-like pattern made of overlapping diamonds and squares. Answer: It has 6 lines of symmetry (3 passing through the vertices, 3 passing between the vertices) due to its hexagonal structure.
9. Draw the following triangles:
- a. A triangle with exactly one line of symmetry.
- Solution: An Isosceles Triangle (but not equilateral).
- b. A triangle with exactly three lines of symmetry.
- Solution: An Equilateral Triangle.
- c. A triangle with no line of symmetry.
- Solution: A Scalene Triangle (all sides different lengths).
Question: Is it possible to draw a triangle with exactly two lines of symmetry? Answer: No. If a triangle has two lines of symmetry, the third median must also be a line of symmetry, making it an equilateral triangle with three lines. You cannot have exactly two.
10. Draw figures with curved boundaries:
- a. Exactly one line of symmetry: A semi-circle or a mushroom shape.
- b. Exactly two lines of symmetry: An ellipse (oval) or a figure-8 shape.
- c. Exactly four lines of symmetry: A flower with 4 petals or a shape like a clover.
11. Copy on squared paper. Complete them so that the blue line is a line of symmetry.