GeoGebra Exercise (with more detail for beginners who want or need help)
This applet shows only some of the many tools in GeoGebra.
A video that follows these instructions is shown below.
At any time, you can use the reverse arrow button in the top right corner to go back and redo.
We start with two points, A and B.
These are free points. You can move them anywhere with the move tool.
They are blue.
When doing constructions, all the tools are based on the compass and the straight edge.
You could use the straight edge to draw a line segment from A to B.
Do that with the segment tool.
Make sure the segment starts and ends on the points A and B.
The compass is used to make circles.
Actually, it is how they anciently measured things anciently (using the radius of the circle).
If you choose the compass tool (the one with the red circle)
and click on it, it says "Select segment or two points for radius, then center point."
Select that tool,
then click on the segment AB itself, and move the circle around until you put its center at A.
Note that a circle is the set of points (or "loci") that are equidistant (same distance, the radius) from a given point (the center).
You should have two circles with centers at A and B, who both have a radius, AB.
These two circles intersect twice.
Use the intersection tool to make the intersection at the top point C, and at the bottom, point D.
These two points are not blue. They are black. This is because they are dependent. They are linked to the intersection of the two circles. If you try to drag them... you can't. Try to drag A or B, and you can.
Draw segments CA, CB, DA, DB, and CD.
Then answer the questions.