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What is a pencil, a compass. and a straightedge in GeoGebra?
Here is a little mathcast (video) explaining the tools we will use ...
Read about it (printable pdf)
Try the tools online or download: BasicConstruct.ggb.
What do we do when it says: Given ...?
Here is a little mathcast (video) explaining how to get the "givens" ...
Read about it (printable pdf)
1. Given a point A ...
2. Given a line m and a point A on m ...
3. Given a line m ...
4. Given an angle α ...
5. Given a circle c ...
How do we do and undo? (a few more techniques)
Here is a little mathcast (video) explaining a few more useful techniques ...
Read about it (printable pdf)
1. Using the Intersection Point Tool
2. Using the Compass Tool  the tool that does:
"I need a circle with center A and with a radius the distance between B and C."
"a.k.a. Take your compass and stick the needle in point B and widen it until it reaches point C.
Now stick the needle in point A and draw a circle."
Seven basic compass and straightedge constructions UPDATED: May 2009 1. Copy a line segment. Complete interactivity
Given: A line segment with start point A and a line with point P on it.
Goal: Construct a on this line with start point P.
(Congruent: the lengths of the segments are equal). 2. Copy a triangle (sidesideside). in progress
Given: A triangle ΔABC and a line with a point P on it.
Goal: Construct a congruent triangle ΔPRS such that the line segment \overline{PR} lies on the given line.
coming soon
3. Copy an angle. Complete interactivity
Given: An angle α with vertex A.
Goal: Copy angle α onto a line with point P so that P is the vertex.
(Congruent: the sizes of the angles are equal). 4. bisect a line segment (in progress)
Given: A line segment \overline {AB} .
Goal: Construct the point C \overline {AB} that is halfway between A and B.
5. Construct a perpendicular (normal). Mathcast updated:30 August 2008
Given: a line m \,\,with a point A \,\,on m \,\,.
Goal: Construct a line n passing through A \,\,and perpendicular (normal) to m \,\,.
6. Bisect an angle
Given: An angle.
Goal: Construct the ray that bisects this angle (divides it into two equal angles).
7. Construct a parallel (uses idea of transversal)
Given: A line m \,\,and a point C \,\, NOT on m \,\,.
Goal: Construct (find) a line p passing through C \,\,and parallel to m \,\,.

Related themes:
 Second Level Constructions? (compass and triangles)
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geometric, construct, construction, straightedge, compass, ruler, geogebra, application, geometry, program