Solutions: Page 239

Questions (Page 239)

7. New Parliament Building (Triangular shape)

• a. Reflection Symmetry: Yes. It looks like an equilateral triangle (or near equilateral). It has 3 lines of symmetry passing through the vertices.
• b. Rotational Symmetry: Yes. Around its centre.
  • Angles: $120^{\circ}, 240^{\circ}, 360^{\circ}$.

8 & 9. Regular Polygons (Table 3 from Chapter 1)

Sequence: The sequence is the counting numbers starting from 3: 3, 4, 5, 6, 7…

10. Koch Snowflake The Koch snowflake is built on an equilateral triangle.

• Lines of Symmetry: 3 (through the main vertices). Correction from Solution PDF: Solution says 3, 6, 6, 6. The base snowflake has 6 lines of symmetry usually, but let’s stick to the text’s specific derivation. The solution PDF lists “3, 6, 6, 6, 6”. This implies as the iterations increase, it stabilizes at 6.
• Angles of Symmetry: Order 6 ($60^{\circ}$).

11. Ashoka Chakra The Ashoka Chakra has 24 spokes.

• Lines of Symmetry: 24.
• Angles of Symmetry: 24 (Order 24).
• Smallest Angle: $360^{\circ} \div 24 = 15^{\circ}$.

Playing with Tiles

b. Use 16 tiles to make figures:

• 1 Line of Symmetry: Arrange them in a long rectangle or an isosceles triangle shape.
• 2 Lines of Symmetry: Arrange them in a 4x4 Square or a Rectangle (e.g., 2x8).