2. Sum of interior angles of a
regular hexagon=
720o
120°
120°
120°
120°
120°
120°

3. The interior angle of a
regular hexagon is 120o.

4. Take a regular
hexagon.

5. We find that the
diagonals
intersect.

6. When the diagonals at the point of intersection are
measured, we find that the angles amount to 360o.

7. This is also found to be the case with other regular polygons (either by
measuring the angles at the point of intersection or measuring the angles of
intersection when the polygon is rotated around a fixed point-a tessellation).

8. (Triangle)

9. (Square)

10. However, this is not the case for all regular
polygons.

11. (Diagonals at
point of
intersection)
(Tessellation: Non-
regular)
(Pentagon)

12. (Tessellation:
Semi-regular,
not regular)
(Diagonals)
(Octagon)

13. As mentioned before, a shape tessellates if it can fit
repeatedly into a pattern around a central point without
overlapping points or gaps.
As you can see from the Octagon:
Its intersecting angles equal 360o, but cannot tessellate:

14. This is because of its interior angle.

15. Each interior angle of a regular shape is equal. This
angle, multiplied by the amount of sides the shape
has, is its angle sum:

16. For a shape to be able to tessellate, the total angle sum created by
rotating the shape around a single point must equal 3600.

17. If the angle sum of the interior angles around that center point
does not equal 360o, then either a gap or an overlap is
created, and the shape cannot tessellate.
135o + 135o135o=405o

18. Computer Applications Used:
Geometer’s Sketch Pad 5
And:
Microsoft Powerpoint