Transcript lesson 1.3
SECTION 1-3 WHAT 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 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 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.