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) |
|||

Hi Kim, 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. -
Draw a line segment and call its length the unit length. I am going to label the ends of the line A and B so that I can refer to them.
- Place the point of the compass at A and the point of the pencil on the other arm of the compass at B.
- Keeping the point of the compass at A draw an arc above the center of the line segment.
- Lift the compass and place the point at B being careful not to change the distance between its ends.
- Use the pencil end of the compass to draw an arc, intersecting the arc drawn in step 3. Call this intersection point P.
- Join A to P and B to P.
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. Penny |