Lesson 6

Building Polygons (Part 1)

Let’s build shapes.

6.1: True or False: Signed Numbers

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

\(4\boldcdot (\text -6) = (\text -6) + (\text -6) + (\text -6) + (\text -6)\)

\(\text -8 \boldcdot 4 = (\text -8\boldcdot 3) + 4\)

\(6 \boldcdot (\text -7) = 7\boldcdot (\text -7) + 7\)

\(\text -10 - 6 = \text -10 - (\text -6)\)

6.2: What Can You Build?

  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.
    1. Measure all the angles in the two shapes you selected. Note: select points in order counterclockwise, like a protractor.
    2. Using these measurements along with the side lengths as marked, draw your triangle and quadrilateral as accurately as possible on separate paper. 


6.3: Building Diego’s and Jada’s Shapes

  1. 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.
  2. 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. 


6.4: Building Han’s Shape

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? 



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 quadrilaterals.  First, sides 11, 5, 7, 14.  Second, sides 11, 7, 14, 5. Third, a convex quadrilateral, sides 11, 7, 5, 14. Please ask for further assistance.

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.