There are two diagrams in the applet. The one on the left relates a point and a line. This part of the applet reckons the triangle inequality. Play with the applet. What is the criteria for determining a triangle, according to the triangle inequality?
The diagram to the right is initially an open figure. Every point in this applet is movable. Drag them around and play for a while. Then, drag D' so that it coincides with D.
In this context, what criteria is necessary to determine a triangle?
If you were given three lengths that satisfied the triangle inequality, how many possible triangles could you construct?