s ection 1-3 w hat is a w idget ?. good definitions are important in geometry. we’ll learn how to...
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SECTION 1-3WHAT IS A WIDGET?
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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?
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What things do all Widgets have in common?
What things do Widgets have that others do not have?
What makes a Widget a Widget?
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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.
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A square is a _______________________
that
________________________
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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.
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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.
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WRITING A GOOD DEFINITION
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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”.
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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.
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EXAMPLE B
Define these terms
Parallel lines
Perpendicular lines
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SPECIAL NOTE
Two lines that do not intersect and are noncoplanar are skew lines
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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.
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RIGHT ANGLE
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ACUTE ANGLE
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OBTUSE ANGLE
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COMPLEMENTARY ANGLES
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SUPPLEMENTARY ANGLES
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VERTICAL ANGLES
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LINEAR PAIR OF ANGLES
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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.