Measuring Up: A Middle School Experience

Triangle Inequality Property

1. Using a pipe cleaner that is 1 foot in length, estimate and mark the location of a point that is about 2 inches from the left endpoint. Bend the pipe cleaner into a right angle at that point. Estimate and mark a point that is about 1 1/2 inches from the right endpoint and bend the pipe cleaner into a second right angle as illustrated. (Be sure your bent pipe cleaner lies entirely within one plane.)

2. Imagine that you will continue to bend the pipe cleaner angles beyond 90°. Will they meet to form a triangle?

3. Why or why not?

4. Repeat this process using angle vertex points that are approximately 2 inches from the left endpoint and 5 inches from the right endpoint.

5. Repeat this process using angle vertex points that are approximately 2 inches from the left endpoint and 4 inches from the right endpoint.

6. Continue trying different vertex points. Then explain in your own words what must be true about the lengths of the 2 end segments of the pipe cleaner in order to be sure that they will produce a triangle.

7. Suppose someone created a pipe cleaner triangle that looked like the one illustrated below, and that when they measured the lengths of a, b, and c they found that the length of a + the length of b was equal to the length of c. How would you respond?

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