I was working on a problem that needed to construct a regular pentagon of a desired length. I couldn’t solve it so checked the solution. The solution in the book was as follows:
- Draw the line $AB$ of desired length of the pentagon.
- Draw the perpendicular line $BC$ that is half the original line.
- Draw hypotenuse $AC$, and extend it as length $BC$ to the point $D$.
- Draw the circle with radius $BD$.
- Now, using a ruler, drawing lines that intersect the circle and are the same length as $AB$ will construct a regular pentagon.
I don’t see why this works. And, then again, this solution uses measurements, how can it be done with just a compass and straightedge without measurements.
P.S. I feel bad for not managing to solve this question. How can I improve myself or is this an indicator that I don’t have a good future at math?
Best Answer
This is how to construct a regular pentagon using only a compass and straightedge without measurements.