writing definitions first – classify what it is second – how does it differ from others in that...
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Writing Definitions
• First – Classify what it is• Second – how does it differ from others in that
classification• EXAMPLE:– A Square is a __________ that ______________
– Classify it How does it differ from others?
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Counter Examples• EXAMPLE– A square is a figure with four equal sides• Is this good?• If not , produce a counter example
• Counterexamples• An example used to prove a statement false• Sketch possible shapes that have the above qualities
but is not a square
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A Good Definition
• A square is a quadrilateral that is equiangular and equilateral– (a 4-sided polygon with equal angles and equal sides)
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Beginning Steps to Creating a Good Definition
• Classify your term. What is it? What class/group does it fit into?
• Differentiate your term. How does it differ from others in that class/group?
• Test your definition by looking for counterexamples.
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Define these termsParallel Lines Perpendicular Lines
Classify, differentiate, test each term
Parallel lines are coplanar lines that do not intersect.
Skew lines are non-coplanar lines that do not intersect
Perpendicular lines are intersecting lines that form 90˚ angles.
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Types of Angles• Acute Angle: an angle
that measures between 0° and 90°
• Right Angle: an angle that measures exactly 90°
• Obtuse Angle: an angle that measures between 90° and 180°
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Angle Relationships
• Complementary Angles: • Two angles whose sum of their
degree measurements equals 90 degrees.
• Supplementary Angles: • Two angles whose the sum of their
degree measurements equals 180 degrees.
50˚
130˚
40˚
50˚
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Angle Relationships
• Congruent Angles: Angles with equal measures.
• Adjacent Angles: angles that share a vertex and a common side but no interior points
• Bisector of an angle: a ray that divides the angles into two congruent angles.
• The endpoint of the ray is the vertex of the angle. is the angle bisector.
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Linear Pair of anglesA linear pair of angles are two angles that are adjacent and supplementary
angles.
If Then m1 m2 180
If two angles form a linear pair,then they are supplementary.
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Vertical Pair of AnglesVertical angles are two angles that are created by two intersecting lines and are opposite each
other.
If two angles are vertical angles,then they are congruent.
< 1 and <3 are a vertical pair of angles< 2 and <4 are a vertical pair of angles
If Then