A triangle has three sides, but not just any set of three lengths will make a triangle. Use this linkage-strip Interactive Activity to answer Problems B1-B5. Note 3
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive, hands-on version of this activity, use linkage strips (or make your own strips).
Fill in the table below. Try to build triangles with the given lengths. Write "yes" or "no" in the fourth column of the table to indicate whether you can or cannot make a triangle from those three lengths. Experiment with different sets of lengths. When you build a triangle, see if you can deform it (change its shape) into a different triangle while keeping the side lengths the same. When you click "Show Answers," the filled-in table will appear below the problem. Scroll down the page to see it. Note 4
Here is the table filled in for the triangles with given lengths and for other sample triangles.
Suppose you were asked to make a triangle with sides 4, 4, and 10 units long. Do you think you could do it? Explain your answer. Keep in mind the goal is not to try to build the triangle, but to predict the outcome.
Come up with a rule that describes when three lengths will make a triangle and when they will not. Write down the rule in your own words.
Suppose you were asked to make a triangle with sides 13.2, 22.333, and 16.5 units long. Do you think you could do it? Explain your answer.
Video Segment In this video segment, Vicky and Lolita write a rule that describes when three lengths will make a triangle. Watch this segment after you have completed Problems B1-B4, and compare your rule with that of the onscreen participants.
What was the first rule that Vicky wrote? How did she and Lolita revise this rule? How does this rule compare with the one that you wrote?
If you are using a VCR, you can find this segment on the session video approximately 9 minutes and 25 seconds after the Annenberg Media logo.
Video Segment In this video segment, Kent describes a different rule for when three lengths will make a triangle. Watch this segment after you have completed Problems B1-B4, and compare your rule with Kent's.
What was Kent's rule? How is it different from Vicky and Lolita's rule? How does this rule compare with the one that you wrote?
If you are using a VCR, you can find this segment on the session video approximately 12 minutes and 50 seconds after the Annenberg Media logo.
Can a set of three lengths make two different triangles?
To answer this question, you will need to know what it means for two triangles to be "different." One definition says that triangles that are "different" cannot have the exact same size and shape. Rotating or reflecting a triangle with the same size and shape does not produce a "different" triangle. Close Tip