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.