Suppose that you have three pieces of wire, each of different lengths, will those pieces of wire ALWAYS create a triangle?
To explore this question, follow the instructions below and use DESMOS to create triangles using the lengths of 3, 4, 5, 6, 8 and 10 units. Record your results in a table similar to the one below (or download the table: Triangles)
- Use the three smallest measurements (of different size), and see if these side lengths can form a triangle.
- Continue to choose three different measurements for side lengths and attempt to make triangles. Be sure to record your attempts (both those that work and those that do not).
| Write down the measurements of each side | Could a triangle be formed? | What is the largest angle type? | |||||
|---|---|---|---|---|---|---|---|
| small | medium | large | yes | no | acute | right | obtuse |
Summary: Compare the lengths of sides that formed a triangle and those that did not. What did you notice about the sum of two sides as it relates to the third side?
Conjecture: Use your data and your summary to make a conjecture about the lengths of the sides of a triangle.
