Question: Can I Tresect An Angle Using This Method?

A new angle trisection method...or complete nonsense

I remember being in 9th grade Geometry and being told that it was 'impossible' to trisect an ange...something I of course took to be a challenge...

I came up with the following system, only to be told by my teacher that what I was doing was wrong...without any explaination as to why.

Take any angle. Using the compass, open it to any length that is shorter than a side. Mark an arc that crosses both sides of the angle. Next, use the straightedge to connect the two points where the arc crosses the legs of the angle. Ignoring the angle for a minute, trisect the new line segment using the standard compass/straightedge construct. Finally, draw a ray from the vertex of the angle through both points which created the trisection points on the line segment.

I believe that the new rays create the trisection of the original angle...

Can you shed light on this????

Answer

Hi there,

I do understand the desire to overcome an impossible challenge. However, in this case, you have not come up with a solution. Your teacher is right to tell you your solution was incorrect.

These are always tough to explain. The reason that your method of trisection doesn't work is that the rays don't divide the angle into three equal angles. How's that for circular reasoning? The reason it doesn't work is because it doesn't work.

I know that's not helpful, but the thing is, you haven't offered any "proof" of why you think it does trisect, so I can't explain why your reasoning is wrong.

So, to give you something helpful, try using your method on a very wide angle - close to 180 degrees. It will become immediately apparent that your method doesn't work. What you will see is that the center angle is very wide, and the two outside angles are much narrower.

Hope that helps. And don't get discouraged - keep looking for challenges to stimulate your brain!