Writing Definitions First – Classify what it is Second – how does it differ from others in that...

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?

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

A Good Definition

• A square is a quadrilateral that is equiangular and equilateral– (a 4-sided polygon with equal angles and equal sides)

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.

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.

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°

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˚

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.

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.

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