Symmetry | Class 6 Mathematics Notes

Symmetry in Regular Polygons

Regular polygons are shapes with all sides and angles equal, such as equilateral triangles, squares, and regular hexagons. These polygons exhibit multiple lines of symmetry. For example, an equilateral triangle has three lines of symmetry, each passing through a vertex and the midpoint of the opposite side. A square has four lines of symmetry: two along the midlines parallel to its sides and two along its diagonals. A regular hexagon has six lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of its sides. This property helps in understanding the balanced nature of regular polygons and is useful in geometry and design. The section explains how to draw these lines of symmetry and verify them by folding or reflection.

📊 Diagram: Figure 9.10 time along a diagonal, as shown in the figure. Again, open it.; Figure 9.11 time along a diagonal, as shown in the figure. Again, open it.; Figure 9.12 time along a diagonal, as shown in the figure. Again, open it.; Figure 9.13 time along a diagonal, as shown in the figure. Again, open it.; Figure 9.14 time along a diagonal, as shown in the figure. Again, open it.; Figure 9.15 time along a diagonal, as shown in the figure. Again, open it.; Figure 9.16 time along a diagonal, as shown in the figure. Again, open it.

🧪 Activity: Draw regular polygons with different numbers of sides. Use a ruler to draw all lines of symmetry and verify by folding the paper along those lines.

🔗 Connection: After understanding symmetry in regular polygons, the chapter discusses symmetry in irregular figures, highlighting differences and exceptions.