Partitioning a Line Segment

Using Rectangles

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


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:


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.

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