# Investigation: Construct segment bisectors

Lesson

### Compass and straightedge construction

Recall that the term bisect means "cut in half".  So to bisect a line segment means to cut the line segment in half or find the halfway point.

#### Steps for construction

1. Start with a line segment $\overline{AB}$AB
2. Place the compass on $A$A.
3. Adjust the width of the compass to what you think looks to be just over half way.
4. Draw an arc on both sides of the line.
5. Keeping the compass the same width, move the compass to point $B$B, and cross the arcs you just created with new arcs.
6. With the straightedge, draw the straight line between the two intersections.
7. This line bisects the segment $\overline{AB}$AB

In fact, this is a very special line, it is called a perpendicular bisector which means it not only cuts the line in half, but the line is perpendicular to the segment (at right angles to it).

### Dynamic software construction

We can also construct a congruent segment using dynamic geometry software.  Press the pause/play button in the applet below to see the steps of the construction in action.  To test the construction, move the points $A$A, $B$B, $C$C, and $D$D around to see that they are always the same length.

Now it's your turn!  Repeat the steps for construction to construct your own set of congruent segments.  Click here to open the applet in a larger web browser window.

#### Steps for construction using technology

 Move Tool Point Tool Line Tool Line Segment Tool Compass Tool Polygon Tool
1. Use line segment tool to draw an arbitrary segment $\overline{AB}$AB.
2. Choose the compass tool, then click on $\overline{AB}$AB to set the radius length to be the same as $AB$AB, then click on center $A$A to draw a circle.
3. Repeat step two with $B$B as the center of the circle.
4. Use the point tool to plot a point $C$C  at the intersection of the two circles.
5. Plot point $D$D at the other intersection.
6. Use the line tool to join points $C$C and $D$D, this is a line that bisects $\overline{AB}$AB.
7. Use the point tool to plot point $E$E at the intersection of $\overline{AB}$AB and $\overleftrightarrow{CD}$CD.  This is the midpoint of $\overline{AB}$AB.
8. Use the Move tool to drag points a $A$A and $B$B and double check that your construction remains.

Save your work!

Be sure to save your construction often, especially if you would like to come back to it at a later time.  If you refresh this page before saving, your work will be lost.

### Outcomes

#### GEO-G.CO.12

Make, justify, and apply formal geometric constructions.