INVESTIGATION: Triangle inequality

Objectives

• To explore the Triangle Inequality

Materials

• Colored straws (at least 7 different colors)
• Scissors
• Paper
• Pencil
• Ruler
• Protractor

Procedure

1. Measure and cut one straw into pieces 2 cm long.
2. Measure and cut a different colored straw into pieces 3 cm long.
3. Measure and cut a different colored straw into pieces 4 cm long.
4. Measure and cut a different colored straw into pieces 5 cm long.
5. Measure and cut a different colored straw into pieces 6 cm long.
6. Measure and cut a different colored straw into pieces 7 cm long.
7. Measure and cut a different colored straw into pieces 8 cm long.
8. Measure and cut a different colored straw into pieces 10 cm long.
9. Use the pieces of straw that you have cut out to create the following triangles and complete the table:
   

Questions

1. Which attempts resulted in the creation of a triangle?
2. For each of the attempts find the sum of the lengths of:
   • Sides 2 and 3
   • Sides 1 and 2
   • Sides 1 and 3
3. For the attempts that created triangles, compare each of the sums you found in the previous question to the remaining side not included in that sum. For example if I am looking at the sum of the lengths of sides 2 and 3 I would compare this number to the length of side 1.  What do you notice?
4. For the attempts that did not create triangles do the same thing. What do you notice?
5. How is this different from the attempts that did create triangles?
6. Based on your observations, what is a general rule you can make for the sides of a triangle?
7. Compare your rule with a friend. Did they come to the same conclusion?
8. With a partner, determine more combinations of side lengths that could create a triangle.
9. Find the area of each of the triangles you were able to create throughout this entire investigation. Use a protractor if necessary.