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?
• EXAMPLE
Counter Examples
– 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 terms
Parallel 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.
40˚
50˚
• Supplementary Angles:
• Two angles whose the sum of their
degree measurements equals 180
degrees.
130˚
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. 𝑂𝑌 is the
angle bisector.
Linear Pair of angles
A linear pair of angles are two angles that are
adjacent and supplementary angles.
If two angles form a linear pair,
then they are supplementary.
m1  m2  180
Vertical Pair of Angles
Vertical angles are two angles that are created by
two intersecting lines and are opposite each other.
< 1 and <3 are a vertical pair of angles
< 2 and <4 are a vertical pair of angles
If two angles are vertical angles,
then they are congruent.