What's Important About Triangles?

Students explore the importance of the side lengths of a triangle and when triangles can or cannot be constructed on the basis of these lengths.

Begin the class by asking the following questions of students:

Can any three lengths be the sides of a triangle? Why or why not?

Inform students that they will be exploring this question in today's lesson. Encourage students to record their predictions in their math journal or on a piece of paper, so they can return to their predictions at the end of the lesson.

Distribute the What's Important about Triangles? activity sheet to each student. Students measure, fold, and tape each strip to make a triangle, if possible.

What's Important About Triangles? Activity Sheet

During a class discussion, ask students to tell what happened when they made the triangles:

• Which measurements were possible?
• What discoveries were made about the lengths of the sides of the triangles?
• Could you categorize the triangles as equilateral, isosceles, or scalene?

Guide students into seeing that the two smaller sides must have a sum that is greater than the largest side. On the activity sheet, figures C, E, and F will not form triangles. Triangles A and H are equilateral triangles; triangles D and G are isosceles triangles; and triangle B is a scalene triangle.

In groups, students can use a spinner to get random triples of side measurements. One person spins the spinner (divided into 6 congruent sectors, 1 through 6) three times. The group determines whether or not those measurements can form a triangle, and if so, what kind (equilateral, isosceles, or scalene.

For example, on the first set of spins, a student might spin 2, 3, and 1. In this case, a triangle would not be formed. On the second set of spins, a student might spin 6, 4, 5. In this case, a scalene triangle would be formed. Students can take turns spinning the spinner. Every member of the group should verify whether or not the three numbers spun actually forms a triangle.

Return to the question asked of students at the beginning of the lesson:

Can any three lengths be the sides of a triangle? Why or why not?

Ask students to compare their predictions with their discoveries from today's lesson. Were any students correct? If so, ask them how they knew the "rule."