triangle inequality
In the bottom figure, let one segment of the triangle rest and drag the third point close to the segment, and then far from the segment. Record the measures. Record the measures of the three sides when you position the point to 8 different locations.
When does the figure cease to determine a triangle?
1. That is, can you express in general terms how the points relate to each other when the points do not make a triangle?
2. Can you express the relationship between the segments when they do not make a triangle?
3. Can you express the relationship between the segments when they DO make a triangle?
Repeat the process for the two remaining points in relation to the static opposite segment. Record your data, and construct a mathematical statement in each case.
Reflect on the statements you wrote. What are the restrictions on the length of any side of a triangle--both its lower bound and its upper bound? In other words, when you have two given lengths, can the third side be as small as 0 and can it be as large as infinity?