# Lesson 15

Building Polygons

### Lesson Narrative

The goal of the lesson is to help students see that sometimes lots of different shapes can be made under given constraints about side lengths, and that at other times, with different constraints, it might be that only one shape is possible or that no shape is possible. In previous lessons, students have considered the requirements for two shapes to be congruent using sequences of transformations. The work here helps students expand their understanding of triangles and, in future lessons, how to identify congruent triangles from limited information about their sides and angles. A focus of the lesson is students using repeated reasoning with specific cases to formulate a general rule (MP8).

Throughout the lesson students work with either cardboard strips and metal fasteners or digital tools along with rulers and compasses. The purpose of the different tools is to help students move toward a mental understanding that does not depend on physical objects.

### Learning Goals

Teacher Facing

• Explain (in writing) how to use circles to locate the point where the sides of a triangle with known side lengths should meet.
• Recognize that four side lengths do not determine a unique quadrilateral, but that three side lengths can determine a unique triangle.
• Use manipulatives to justify when it is not possible to make a triangle with three given side lengths.
• Use manipulatives to show that there is a minimum and maximum length the third side of a triangle could be, given the other two side lengths.

### Student Facing

Let’s build shapes.

### Student Facing

• I can show that the 3 side lengths that form a triangle cannot be rearranged to form a different triangle.
• I can show that the 4 side lengths that form a quadrilateral can be rearranged to form different quadrilaterals.
• I can show whether or not 3 side lengths will make a triangle.