Lesson 6Building Polygons (Part 1)

Learning Goal

Let’s build shapes.

Learning Targets

  • 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.

Warm Up: True or False: Signed Numbers

Problem 1

Decide whether each equation is true or false. Be prepared to explain your reasoning.

Activity 1: What Can You Build?

Problem 1

open applet in presentation mode

  1. Use the segments in the applet to build several polygons, including at least one triangle and one quadrilateral.

  2. After you finish building several polygons, select one triangle and one quadrilateral that you have made.

    • Measure all the angles in the two shapes you selected. Note: select points in order counterclockwise, like a protractor.

    • Using these measurements along with the side lengths as marked, draw your triangle and quadrilateral as accurately as possible on separate paper.

Print Version

Your teacher will give you some strips of different lengths and fasteners you can use to attach the corners.

  1. Use the pieces to build several polygons, including at least one triangle and one quadrilateral.

  2. After you finish building several polygons, select one triangle and one quadrilateral that you have made.

    • Measure all the angles in the two shapes you selected.

    • Using these measurements along with the side lengths as marked, draw your triangle and quadrilateral as accurately as possible.

Activity 2: Building Diego’s and Jada’s Shapes

Problem 1

Diego built a quadrilateral using side lengths of 4 in, 5 in, 6 in, and 9 in.

open applet in presentation mode

  1. Build such a shape.

  2. Is your shape an identical copy of Diego’s shape? Explain your reasoning.

Print Version

Diego built a quadrilateral using side lengths of 4 in, 5 in, 6 in, and 9 in.

  1. Build such a shape.

  2. Is your shape an identical copy of Diego’s shape? Explain your reasoning.

Problem 2

Jada built a triangle using side lengths of 4 in, 5 in, and 8 in.

open applet in presentation mode

  1. Build such a shape.

  2. Is your shape an identical copy of Jada’s shape? Explain your reasoning.

Print Version

Jada built a triangle using side lengths of 4 in, 5 in, and 8 in.

  1. Build such a shape.

  2. Is your shape an identical copy of Jada’s shape? Explain your reasoning.

Activity 3: Building Han’s Shape

Problem 1

Han built a shape using side lengths of 3 in, 4 in, and 9 in.

open applet in presentation mode

  1. Build such a shape.

  2. What do you notice?

Print Version

Han built a polygon using side lengths of 3 in, 4 in, and 9 in.

  1. Build such a shape.

  2. What do you notice?

Lesson Summary

Sometimes we are given a polygon and asked to find the lengths of the sides. What options do you have if you need to build a polygon with some side lengths? Sometimes, we can make lots of different figures. For example, if you have side lengths 5, 7, 11, and 14, here are some of the many, many quadrilaterals we can make with those side lengths:

Three polygons of differing shapes.

Sometimes, it is not possible to make a figure with certain side lengths. For example, 18, 1, 1, 1 (try it!).

We will continue to investigate the figures that can be made with given measures.