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Understand what makes a figure a widget, learn to write precise definitions in geometry, differentiate geometric tools like protractors and squares, and practice creating and testing definitions. Explore parallel, perpendicular, and skew lines, and define angles like right, acute, obtuse, complementary, supplementary, vertical, and linear pairs.
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Good definitions are important in Geometry. We’ll learn how to write good definitions in this lesson. Which figure is a widget in the last group?
What things do all Widgets have in common? What things do Widgets have that others do not have? What makes a Widget a Widget?
A protractor is a geometric tool used to measure angles. You classify what a protractor is. Then you tell how it differs from other geometric tools.
A square is a _______________________ that ________________________
Once you have written a definition you should test it. Try to look for a counterexample. That means you should try to create a figure that fits your definition but isn’t what you are trying to define. Check your definition of a square.
Example A • Everyone knows, “A square is a figure with four equal sides. What’s wrong with this definition? • Sketch a counterexample. • Write a better definition of a square.
Before you write a few definition here are some special markings we use for parallel lines. The same number of arrow marks indicate parallel lines. The || mean “is parallel to”.
Before you write a few definition here are some special markings we use perpendicular lines. The small square in the corner of the angle indicates that it measures 90o. The symbol ┴ means “is perpendicular to”.
Example B • Define these terms • Parallel lines • Perpendicular lines
Special Note • Two lines that do not intersect and are noncoplanar are skew lines
Defining Angles • Write a definition for each bold faced term. Make sure your definitions highlight important differences. • Trade definitions and test each other’s definitions for counterexamples. • If another group member finds a counterexample to one of your definitions, write a better definition. As a group, decide on the best definition for each term. • As a class agree on common definitions. Add these to your notebook. Draw and label a picture to illustrate each definition.
Example • Use the picture at the right to write a definition for a pair of linear angles by using the names of two angles in your definition.
