Quandaries and Queries
I am a non-traditional college student who hasn't had geometry since elementary school.
I would like to know how to draw different shapes:
Regular Octagon with sides of length, 1 unit
Equilateral Triangles, with sides of length 1 unit
Regular Hexagons, with sides of length 1 unit
Isoseles Triangles, with hypotenuse of length 1 unit
(I figured out the square)
By draw I assume you mean that you have to construct these shapes with a straight edge and a compass.
To construct a regular octagon you need to construct a 45 degree angle.
If you draw a diagonal in the square you have already constructed then you have a 45 degree angle.
For both an equilateral triangle and a regular hexagon you need to construct a 60 degree angle. An equilateral triangle, and hence a 60 degree angle can be construct as follows.
The lengths |AB|, |BP| and |PA| are equal and hence the triangle PAB is an equilateral triangle and the angles PAB, ABP an BPA are each 60 degree angles.
In your last problem I assume you want an isosceles right angles triangles, with hypotenuse of length 1 unit. One of the figures you have already drawn can be cut up into pieces that are isosceles right angles triangles with hypotenuse of length 1 unit.