Section 1-3 What is a Widget?

1. Section 1-3What is a Widget?

2. 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?

3. What things do all Widgets have in common? What things do Widgets have that others do not have? What makes a Widget a Widget?

4. 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.

5. A square is a _______________________ that ________________________

6. 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.

7. 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.

8. Writing a Good Definition

9. 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”.

10. 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”.

11. Example B • Define these terms • Parallel lines • Perpendicular lines

12. Special Note • Two lines that do not intersect and are noncoplanar are skew lines

13. 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.

14. Right Angle

15. Acute Angle

16. Obtuse Angle

17. Complementary Angles

18. Supplementary Angles

19. Vertical Angles

20. Linear Pair of Angles

21. 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.