EMAT 6700

Trisecting a Segment

Use geometer's sketchpad to trisect a segment.

Trisect segment AB.

1.  Draw segment AM.

3.  Construct a point X on segment AM.  Construct a segment AX.  Select point X and segment AX.  Construct circle by center and radius.  Construct the intersection of circle X and segment AM.  Label the intersection point Y.

4.  Select circle X.  Hide the circle.  Select point Y and segment AX.  Construct circle by center and radius.  Construct the intersection of circle Y and segment AM.  Label the intersection point Z.

5.  Select circle Y.  Hide the circle.  Select point Z and point B.  Construct segment ZB.

6.  Select segment ZB and point Y.  Construct a parallel line.  Construct the intersection of segment AB and the parallel line.  Label the intersection point Q.

7.  Select segment ZB and point X.  Construct a parallel line.  Construct the intersection of segment AB and the parallel line.  Label the intersection point P.

Because parallel lines cut off congruent segments on transversals, segment AP, segment PQ, and segment QB are all congruent to each other.  Hence, segment AB has been divided into three congruent segments or trisected.