Partitioning a Line Segment

Using Rectangles

(1/3's,1/5's,1/7's,and Even Partitions)

by

Troy Morris

Given line segment AB, construct perpendicular lines to the segment through the given endpoints. Choose a point D above the segment on either perpendicular and construct a parallel line to segment AB.

Next, label the remaining intersection point D and construct segments AD,DC, and BC. You may also hide the lines to finalize your construction of a rectangle.

Construct the midpoint of segment CD and label it M. Construct segments DB and AM. Label their intersection point G.

Construct the perpendicular line segment from G to segment AB. Label this point X.

AX = (1/3)AB

Click Here for the proof.

To continue on bisecting the segment,click on the following:
1/5's

1/7's

The even partitions are constructed by using the same procedures as above. The only difference coming with the construction of A to the midpoint of DC. That line segment should simply be another diagonal, AC, intersecting the diagonal BD. From there, the order of partitioning the segment remains constant to that above.

Return to my homepage