How can you divide an angle into 3 equal angles? You may only use a straightedge and a compass to achieve this.

(This means : You have an angle A, you divide Angle A into 3 Angles B,C,D. And B=C=D=A/3)

Note: vohonam clarified that the problem actually only gives you a straightedge, not a ruler.

ok i got it!!!!!!!! omg im soooo happy i found it!!!!!!!! here i go step by step (sorry for this but im a horible writer)

1. extend the lines on the angle

2. set your compass to a large gap

3. mark equil lengths from the origin of the rays that make the angle (like you do in the first step of copying an angle)

4. draw a line from the two pints that you just made

5. copy the line to another peice of paper see sub steps labeled [num.num.]
5.1. draw a line longer then the one you want to copy
5.2. set your compass to the length of the line
5.3. put the point of the compass on one end
5.4. mark the spot that the pencil is on

6. divide the line into 3 equil segments note: this IS writen very confuisingly (sorry)
6.1. make a ray starting at the end of the line you just made in step 5 make it about a 60deg angle for ease of the next steps, make the line below the line made in step 5
6.2. set your compass to a small length close to 1/3 the length of the line you made in step 6.1 (exactness dosnt count here as long as there all the same length)
6.3 put the needle end of your compass on the origin of the two lines
6.4 make a mark on the line made in 6.1
6.5 move your compass to the mark you just made, make another mark
6.6 move to the mark made in 6.5 and make one last mark
6.7 make a line from the mark made in step 6.6 to the mark made in step 5.4
6.8 now, copy the angle made from the lines made in steps 6.7 and 6.1, therfore makeing a line parallel to the line made in step 6.7
6.9 copy it again this time so that you make a parallel line that goes trough the point made in 6.4
6.10 now the three segments of the line made in step 5 are equil lengths!!! yay!

Posted by James on 2002-10-25 20:30:10