SECTION 1-3WHAT IS A WIDGET?

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.

1. You classify what a protractor is.2. 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 || mean “is parallel to”.

The small square in the corner of the angle indicates that it measures 90o.

The symbol ┴ means “is perpendicular to”.

Before you write a few definition here are some special markings we use perpendicular lines.

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

1. Write a definition for each bold faced term. Make sure your definitions highlight important differences.

2. Trade definitions and test each other’s definitions for counterexamples.

3. 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.

4. 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.