 # Investigation: Construct congruent segments

Lesson

### Compass and straightedge construction

To construct congruent line segments with a compass and straightedge, follow the instructions below.  Play and pause the video at each step to help you.

#### Steps for construction

1. Start with the line segment $\overline{AB}$AB on the page that you want to copy.
2. Mark a point on the page where you want the start of the copied line segment. Call this point $C$C.
3. Set the compass width to the length of  $\overline{AB}$AB.
4. Without changing the compass width, move the compass to $C$C
5. Draw an arc. The endpoint of the new line segment can be anywhere on the arc.
6. Choose a point ($D$D) on the arc and draw $\overline{CD}$CD with the straightedge.

### 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.  This is sometimes referred to as a drag test.

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. Use the point tool to plot a third point $C$C anywhere on the screen.
3. 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 $C$C to draw the circle.
4. Use the point tool to plot a point $D$D  anywhere on circle C.
5. Use the segment tool to join points $C$C and $D$D, this is a line segment congruent to $\overline{AB}$AB
6. Use the Move tool to drag point $A$A , $B$B, $C$C, and $D$D and double check that your construction passes the drag test.

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.1

Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.

#### GEO-G.CO.12

Make, justify, and apply formal geometric constructions.