Lesson 6

Lesson 6: Exploring Parallel Lines

 

Focus

 

 

In earlier lessons you looked at various examples of patterns in games and puzzles. You analyzed specific patterns of moves in an actual game or patterns in the puzzle to develop winning strategies. Inductive reasoning is not only helpful in determining patterns in game play; it can also be used to identify geometric relationships in the design of the game or puzzle.

 

Consider the game fox and geese. It is played on a cross-shaped board with 33 holes. The holes are connected by straight and diagonal lines. This game dates back to the Middle Ages in Europe. There are many versions of this game. For instance, some First Peoples have a game that, when translated, is called “playing leader.” In Japan, the game is known as juroku musashi or “sixteen soldiers.”

 

The design of the game surface is crucial to how the game is played. The position of the holes and the arrangement of the lines determine how the fox and the geese can move. Many factors go into successful design. Relationships between elements in the design, such as angles and lines, are carefully examined. This information is vital to ensure that the design can be recreated.

 

This lesson will help you answer the following inquiry questions:

• What relationships can be identified between pairs of angles formed by transversals and parallel lines in various designs?

• How can inductive reasoning be used to make conjectures about the relationships of angles formed when a line intersects a pair of parallel lines?

Assessment

• Try This 4
• Lesson 6 Assignment

All assessment items you encounter need to be placed in your course folder.

 

Save a copy of the Lesson 6 Assignment to your course folder. You will receive more information about how to complete the assignment later in this lesson.

 

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