Section 1-3 What is a Widget?

Good definitions are important in Geometry 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.

Writing a Good Definition

The same number of arrow marks indicate parallel lines. 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.

Right Angle

Acute Angle

Obtuse Angle

Complementary Angles

Supplementary Angles

Vertical Angles

Linear Pair of Angles

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.