Lesson 11

1. Lesson 11

1.5. Explore 2

Module 2: Lesson 11

Module 2: Logic and Geometry

Self-Check 3

Complete “Practising” questions 6, 7, 11, and 13 on pages 100 and 101 of your textbook. (Note: For question 6, a loonie has 11 sides). Answer

Polygons are used in many different designs, both human-made and in nature. They can be arranged to create tessellations or other repeating patterns in custom floor tile designs, puzzles, and art, or polygons can be used as sweet storage for insects.

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Planning the layout of the design is very important, especially with a complex pattern. Mistakes can be costly, time consuming, and, in nature, maybe even fatal. Amaya looked at a tessellation that involved only one type of polygon. Tessellations can be created that use more than one type of polygon in their design.

Read “Example 3: Visualizing tessellations” on page 98 of your textbook. How is an understanding of angles in polygons used to solve the problem?

Self-Check 4

Complete “Your Turn” on page 98 of your textbook. Answer

Enrico is a structural engineer who is building a house that incorporates unique designs. He really likes the idea of putting a pentagonal door in his house. As a structural engineer, however, he realizes that he will need to add two supports to the pentagon so the door does not collapse.

Did You Know?

Richard Buckminster Fuller (1895–1983), aka “Bucky,” was an American architect and inventor fascinated by nature’s principles of design. He developed the geodesic dome design. His design has been used all over the world including the Montreal Biosphere for Expo 1967.

The influence of his design can also be seen in the official design for the 1970 World Cup’s soccer ball. Fuller even has a carbon molecule named after him! In 1985, scientists discovered a molecule made up of 60 carbon atoms (C60) that were arranged in a structure similar to Fuller’s geodesic dome. This earned the molecules the names of fullerenes and buckyballs.

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This is an image of a molecular model of a carbon molecule called fullerenes.

He makes a quick sketch of his door design.

This is an image of a pentagon with an isosceles triangle in the inside.

To create an accurate design drawing for his contractor, he needs to determine all of the angles. He knows how to find the interior angles of the pentagon as shown.

Enrico does not know the measures of the angles formed by the two supports in the door. Watch the animation Door Design to see how Enrico determines one of these missing angle measurements.