Shape

More Triangle Recipes--Challenge: More Spaghetti Triangles

In this section, you will investigate two additional strategies for constructing and/or duplicating triangles. Directed activities Angle-Angle-Angle and Side-Side-Angle raise the issue of insufficient conditions, that is, circumstances in which a strategy does not determine a unique figure with the proper features.

Materials needed: Dry spaghetti

Fraction Circle pieces, not halves

Part I

v Select any two pieces of spaghetti and one of the fraction circle pieces. Use the two pieces of spaghetti as two sides of a triangle with the fraction circle piece not as the included angle between them. Break a piece of spaghetti piece to complete the triangle.

v Select a second set of pieces (two spaghetti pieces and one fraction circle piece) that are congruent to those already chosen. Can you create a different triangle than the first one you created? Note: Angle placement remains the same.

v Repeat at least 6 times. Were you able to create different triangles with the same set of three pieces? Explain. What conjectures can you and your group make about two specific sides and a non-included angle of a triangle?