We’ll explore a method for drawing a triangle that has three specific side lengths. Your teacher will give you a piece of paper showing a 4-inch segment, as well as some instructions for which strips to use and how to connect them.

1. Follow these instructions to mark the possible endpoints of one side:

   1. Put your 4-inch strip directly on top of the 4-inch segment on the piece of paper. Hold it in place.

   2. For now, ignore the 3-inch strip on the left side. Rotate it so that it is out of the way.

   3. In the 3-inch strip on the right side, put the tip of your pencil in the hole on the end that is not connected to anything. Use the pencil to move the strip around its hinge, drawing all the places where a 3-inch side could end.

   4. Remove the connected strips from your paper.

2. What shape have you drawn while moving the 3-inch strip around? Why? Which tool in your geometry toolkit can do something similar?

3. Use your drawing to create two unique triangles, each with a base of length 4 inches and a side of length 3 inches. Use a different color to draw each triangle.

4. Reposition the strips on the paper so that the 4-inch strip is on top of the 4-inch segment again. In the 3-inch strip on the left side, put the tip of your pencil in the hole on the end that is not connected to anything. Use the pencil to move the strip around its hinge, drawing all the places where another 3-inch side could end.

5. Using a third color, draw a point where the two circular marks intersect. Using this third color, draw a triangle with side lengths of 4 inches, 3 inches, and 3 inches.