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Lesson 11

1. Lesson 11

1.7. Connect

Module 2: Lesson 11

Module 2: Logic and Geometry

 

Connect
 
Project Connection
 
This is a photo of a teenage girl wearing a hard hat.

iStockphoto/Thinkstock

Throughout this module, you have used reasoning to solve problems relating to games, puzzles, patterns, and designs containing parallel lines and polygons. You used reasoning to identify different strategies, determine missing measurements, and verify given information.

 

You are now ready to complete the project for this module. Open the Module 2 Project and start designing!

 

Going Beyond
 

Assume you have an unlimited number of squares and equilateral triangles all with the same side length available to you. In this problem, you want to build larger convex polygons using the squares and triangles you have available. Recall that in convex polygons, each interior angle measures less than 180°.

 

This is an illustration of convex and non-convex polygons.

 

You can think about it like this:

  • If you can put an elastic band around the polygon and there are no empty spaces, you have built a convex polygon.

  • If you have empty spaces when you put an elastic band around the polygon, you have built a non-convex polygon, which is not allowed.

    This illustration shows two non-convex polygons with empty spaces formed when an elastic band is placed around each polygon.

 

Use the Building Polygons applet to build convex polygons with 7, 8, 9, 10, and 11 sides. Alternatively, you can cut equilateral triangles and squares with the same side length out of cardboard or paper. Use the applet or your paper triangles and squares to answer the following questions.

 

 

This is a screenshot for Building Polygons.

  • Can you build convex polygons with more than 11 sides?

  • What is the maximum number of sides that a convex polygon formed by equilateral triangles and squares can have? What is the measure of each interior angle in this polygon?

Answer