Vocabulary
Term
Auxiliary Line
Base
Definition
A line that is added to a diagram
to help explain relationships in
proofs.
The side to which an altitude is
drawn, or is considered to be
drawn.
Base Angle
Angles that are opposite the equal
sides.
Conjecture
A conclusion reached by using
inductive reasoning.
Indirect
Reasoning
All possibilities are considered
and all but one is proved false.
The remaining possibilities must
be true.
Inductive
Reasoning
Reaches conclusions based on a
pattern of specific or past events.
Isosceles
Trapezoid
A trapezoid whose non parallel
opposite sides are congruent
Rectangle
A parallelogram with four right
angles.
Reflexive
Property
Let a be any real number.
then a = a
Remote Interior
Angle
Diagram/Example
Two nonadjacent interior angles
corresponding to each exterior
angle of a triangle.
Example: As you walk down the street you see many people
holding unopened umbrellas. You make the conjecture that
the forecast must call for rain.
Example: Sam spent more than $60 on two books. Prove
that at least one book costs more than $30.
Proof: Suppose neither costs more than $30. Then he spent
no more than $60. Since this contradicts the given
information, at least one book costs more than $30.
Example: You see four people walk into a building, each
person leaves with a small bag with food. You use inductive
reasoning to conclude this building contains a restaurant.
Consecutive
Angles
Two angles that share a common
side
Coordinate
Proof
A figure is drawn on a coordinate
plane and the formulas for slope,
midpoint and distance are used to
prove properties of the figure.
Counter
Example
Exterior Angle
of a Polygon
An example that shows a
statement is false.
Formed by a side and an
extension of an adjacent side of a
polygon.
Kite
Quadrilateral with two pairs of
consecutive sides congruent and
no opposite sides congruent.
Legs
The two congruent sides of a
triangle or the two sides that
forms a 90o angle in a right
triangle.
The segment that joins the
midpoints of the nonparallel
opposite sides of a trapezoid.
Midsegment of
a Trapezoid
Rhombus
Square
Symmetric
Property
Parallelogram with four
congruent sides.
Parallelogram with four
congruent sides and four right
angles.
Let a and b be any real number.
If a = b, then b = a.
Statement: All apples are red.
Counter Example: A Granny Smith Apple is green.
Flow Proof
Indirect Proof
Arrows show the logical
connections between the
statements.
A convincing argument that uses
indirect reasoning
Example: Club A and B have less than 20 members. Club B
has 10. Prove Club A has less than 10 members.
Proof: Suppose Club A has 10 or more members. Then Club
A and B have 20 or more members. Since this contradicts the
membership total of less than 20, Club A must have less than
10 members.
Opposite
Angles
Two angles of a quadrilateral that
does not share a side.
Opposite Sides
Two sides of a quadrilateral that
does not share a vertex.
Parallelogram
A quadrilateral with two pairs of
parallel sides.
Proof
Theorem
Transitive
Property
A convincing argument using
deductive reasoning.
A conjecture that is proven.
Let a, b and c be any real number.
If a = b and b = c, then a = c.
Trapezoid
Two Column
Proof
Quadrilateral with exactly one
pair of parallel sides.
The statement and reasons of the
proof are aligned in columns.
Example: Theorem - Vertical angles are congruent.