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5.
When the diagonals at the point of intersection aremeasured, we find that the angles amount to 360o.
6.
This is also found to be the case with other regular polygons (either bymeasuring the angles at the point of intersection or measuring the angles ofintersection when the polygon is rotated around a fixed point-a tessellation).
12.
As mentioned before, a shape tessellates if it can fitrepeatedly into a pattern around a central point withoutoverlapping points or gaps.As you can see from the Octagon:Its intersecting angles equal 360o, but cannot tessellate:
14.
Each interior angle of a regular shape is equal. Thisangle, multiplied by the amount of sides the shapehas, is its angle sum:
15.
For a shape to be able to tessellate, the total angle sum created byrotating the shape around a single point must equal 3600.
16.
If the angle sum of the interior angles around that center pointdoes not equal 360o, then either a gap or an overlap iscreated, and the shape cannot tessellate. 135o + 135o135o=405o
17.
Computer Applications Used:Geometer’s Sketch Pad 5And:Microsoft Powerpoint
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