[F.2數學] 快入黎幫幫手><><>

1. Explain why six identical equilateral triangles can form a regular hexagon.
Refer to the formation diagram of a regular hexagon here:
http://en.wikipedia.org/wiki/File:HexagonConstructionAni.gif
In the construction diagram, we can see that the six identical equilateral triangles are drawn one after the other next to each other, with the resulting regular hexagon having vertices on a circle of radius equal to the length of each side of the six triangles, which is also the side length of the regular hexagon.
The six identical equilateral triangles each sustain an angle of 60 at the centre to give a total of 360. This is another proof that they can form the regular hexagon.

2. If a figure has five sides of equal length , can we conclude that itis a regular pentagon? Explain with an example.
A figure with five sides of equal length is not necessarily a regular pentagon unless all the five angles are obtuse angles of 108.
An example is one with angles in order of 36, 252, 36, 108 and 108.ie two acute, one reflex and two obtuse angles and five equal sides. As only the sides are the same and not the angles , it cannot be a regular hexagon.