Geogebra Exploration 1: Three points
Problem Set
1. Play around with the application: drag A, B, and C around the plane. Click the boxes and see what they do.
2. Begin this exercise by first hiding the segments. Position the points in such a way where all three appear to be collinear.
Then, click the boxes and record the results (given that the values are lengths of segments).
3. Unclick the boxes again. Now, move one point (easiest to move the middle one) so that the points are non-collinear. What relationship do the three points have now?
4. How far off the line did you have to move the point in order to establish this relationship? Discuss this with your group. Be as precise with your language as possible.
5. Freely click the boxes to help visualize the relationship. When you do, what do you notice about the lengths that are given? Record the results.
6. What is different about the results that you wrote from Question 2?
7. Express a general statement about the relationship between the lengths of the segments when the points are collinear.
8. Express a general statement about the relationship between the lengths of the segments in the second relationship.