Definitions
Chapter 1

Conjecture
– an unproven statement that is based on
observations.

Inductive Reasoning

Counterexample
– a process that includes looking
for pattern to make statements.
– an example that proves a conjecture
false.

Collinear

Coplanar

Segment

Ray

Opposite Rays
– two or more points that lie on the same line.
– two or more points that lie on the same plane.
– part of a line consisting of endpoints and all the
points between those points.
– Part of a line that consists of a point, the initial
point, and all the points on the line that extend in one
direction.
– two rays with a common initial point and
form a line.

Parallel Lines –
two or more lines that are coplanar and
do not intersect.

Perpendicular Lines –
two lines that intersect to form a
right angle.

Skew Lines –
two or more lines that are noncoplanar and do
not intersect.

Postulates (axioms) –
rules or statements accepted
without proof.

Theorems
– rules or statements that have to be proven to be
accepted.

Angle -
two different rays, the sides, that have the same
initial point, the vertex.

Adjacent Angles –

Linear Pair –
two angles that share a common vertex
and side, but have no common interior points.
two adjacent angles whose noncommon sides
are opposite rays.

Acute Angle –

Right Angle –

Obtuse Angle –
an angle whose measure is greater than zero
and less than ninety degrees.
an angle whose measure is ninety degrees.
an angle whose measure is greater than
ninety and less than one hundred eighty degrees.

Straight Angle –

Congruent –

Midpoint –
an angle whose measure equals one
hundred eighty degrees.
segments or angles that have the same measure.
the point in a segment that divides the segment
in half.

Segment Bisector

Angle Bisector

Vertical Angles
– a segment, ray, line, or plane that
intersects a segment at its midpoint.
– a ray that divides an angle into two
adjacent angles that are congruent.
– two angles whose sides form two pairs of
opposite rays.

Complementary Angles

Supplementary Angles
– two angles whose sum of their
measures is ninety degrees (complements).
– two angles whose sum of their
measures is one hundred eighty degrees (supplements).
Chapter 2
 Deductive
Reasoning
–
using facts, definitions, and
properties in a logical order to prove a statement
.