This document provides instructions for dividing a line segment into an equal number of parts using the intercept theorem. The steps are to: 1) Draw a line from one endpoint of the segment making an acute angle. 2) Take equal measurements along this line using a compass. 3) Join the last measurement point to the other endpoint to create a reference line. 4) Draw lines parallel to the reference line from each measurement point to divide the segment into equal parts. This process works for any number of desired parts.

1. This presentation has been made for you by
FRANCISCO GUIJARRO BELDA
From Isaac Albéniz Secondary School
Leganés. Madrid. Spain.

2. HOW TO DIVIDE A LINE SEGMENT INTO ANY NUMBER OF
EQUAL PARTS
1) This process is based on the “Intercept Theorem”, also known as “Thales
Theorem”. Let s imagine we have a line segment AB already given

3. 2) Draw a line from either point A or B (in red color in the image below). In this
example we are going to work from A. The line must make an acute angle with
AB.

4. 3) Let´s imagine we want to divide AB into five equal parts. Let´s take five
measurements over the red line with the compass. It doesn´t matter how long these
measurements are as long as all of them are equal

5. 4) Join the last point you got with the compass in the red line to point B. This new
line (in blue color) is going to be our reference from now on.

6. 5) Draw, from every point in the red line, a line parallel to 5B, that is, to the blue line.
Work with the set square as you can see in the picture below.

7. 6) Once you have finished drawing the parallels, you are done. Keep in mind that this
process is applicable to any number of parts, the only thing you have to do is to
change this number while working with the compass.