Open the GSP application and you should see a screen with a toolbar on the left. On the toolbar you see the select tool(an arrow), the point tool, the circle tool, the segment tool, the labelling tool (a hand with the letter A on it) and the information tool (a questionmark).
If you move the cursor over to the selection tool and hold down the mouse, you will see that the menu expands. The other options allow you to rotate and expand the figure you construct. For now we will stick with the regular arrow, which allows you to select parts of the figure.
The point tool allows you to draw points in any figure you are working on.
The circle tool, as you might expect, will allow you to construct circles.\\If you move the cursor over to the segment tool and hold down the mouse, you will see that the menu expands. The other options allow you to draw rays and lines.
The labelling tool allows you to put labels in the figure. It will for instance label points as A,B,C, etc.
The information tool gives object information.
We will explore some of these features through an exercise.
1. Make sure that you have selected the line segment. Now draw a linesegment by clicking and dragging the mouse.
2. There will be two black squares on the line segment. This means that the line segment has been selected as an object. This allows us to do measurements on the line segment. Go to measure on the menu bar at the top of your screen. Select length there. The measurements of the length will be displayed as mAB = .. It is often useful to display the labels in the figure to avoid confusion over what it is you are measuring. So select the labelling tool and point and click on the endpoints of your line segment. One of them should now be labelled A, and the other one as B. Note that if you click on one of the labels, you can drag it around to position it in a convenient place.
3. Go back to the select tool and make sure that the line segment has been selected. Now go to construct on the menu at the top of the screen and select `'point at midpoint''. You should now have the midpoint drawn on the line segment.
4. You can select and deselect multiple objects if you hold down the shift key as you do the selections. The midpoint should still be selected, so as you hold down the shift key select the line segment. How do you know if the cursor is pointing to something so that you can select it? The cursor will go from a slanted arrow to a horizontal arrow. Furthermore, on the bottom of your screen it will tell you what the cursor is pointing at.After selecting the midpoint and the line segment, go to construct and select `'perpendicular line''. You have now constructed a perpendicular bisector to the line segment you first drew.
5. For the next step of the problem we want to pick a point on the perpendicular bisector. You can either select the line and go to construct and choose `'point on object'' or you can go to the point tool and draw a point on the line free-hand. After drawing in this point label it. You should have C as the label for the midpoint of the line segment and D as the label for the point on the line.
6. We want to construct line segments AD and BD. There are two ways of doing this. (Holding down the shift key) select two of the points and construct a line segment between them using the construct menu. Alternatively, you can use the segment tool and draw the segments free hand.
7. Select each line segment in turn and compute their length using the measure menu.
8. Select points B, A and D in that order. Now go to measure and select angle. This measures angle A. Similarly select points A, B and D (in that order!) and measure angle B.
9. What do you notice about the lengths AD and BD? What do you notice about the measures of the angles A and B?
10. This is the same exercise as we did with paper in 3.6. The nice feature of this computer program is that you can turn this into a dynamic example. For instance: select the point D and drag it up and down the perpendicular bisector and notice what happens to the lengths of the line segments and the measures of the angles.
11. Notice that you can also select for instance the point B and drag that to another point on the screen. Because C is defined as the midpoint of AB, we see that the entire picture stays intact. Try this!
12. Find the midpoint of AD and construct the perpendicular bisector. Similarly, find the midpoint of BD and construct the perpendicular bisector. What do you notice about the three perpendicular bisectors?
13. You should have found that the three perpendicular bisectors intersect in one point. If you select point A, B or D and move it around a little bit, does this change this property? What happens to the intersection point when you go from an acute to an obtuse triangle? Can you guess where the intersection point should lie when when you have a right triangle?