TO DIVIDE A LINE

To divide a line segment into equal number of parts using a compass only, Example Divide the line into 5 parts,

Steps of construction:

1) Draw a line segment AB of any length.

2) Draw any ray AX, making an acute angle (angle less than 90°) with AB.

3) Now take a compass and with any length draw an arc cutting the line ray AX at point 1, mark this point as A1.

4) With the length A1, Draw 4 more arcs with centres 1, 2, 3, 4 as shown and mark those intersecting points as A2, A3, A4, A5 as shown below.

AA1 = A1A2 = A2A3 = A3A4 = A4A5

5) Now join BA5, it will form a triangle, similarly draw lines from the remaining 4 arcs parallel to line BA5 as shown.

6) The above points divide the line AB into equal parts (You can cross check by measuring the distances).