0504 Measuring two segments
Task:
Let the segments AB and CD be given. Decide which segment is larger by editing.
Analysis:
In the P-model the size of the two segments does not appear to differ. Thus, we really need this construction. (Later, if we are going to measure the length of the segment, the question can also be decided by comparing their metrics.)
First, we must interpret the relation <, =, and > between the segments.
- Two segments are equal if those can be transferred to each other by congruence transformations (axial reflections).
- The larger segment of two segments on a ray with a common starting point is the one which contains the endpoint of the other segment (this endpoint is different from the starting point of the ray).
- The <,> relation between two different segments can be decided based on the <,> relation between segments that are congruent with them and have a common starting point on a ray.
Solution:
Construct a circle with radius AB und centre C. For this, find the intersection point M with the ray [CD). Three possible answers can be given to compare the segments with one of the signs <, =, >. They can be selected, for example, as follows:v=If(Distance(M, D) < 0.1, "=", If(IsInRegion(D, s), ">", "<"))
Principally, we could have asked the previous question like this: D≟M. However, let us be much more lenient now. It would be very difficult to adjust two randomly picked moveable segments, so that we get the true answer to the D≟M question. Here we can read about the detectability of the coincidence between points, in general the reliability of GeoGebra.