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Geometry Definitions
POINTS, LINES, and PLANES
Points
• Points C, M, Q
• A point is the most fundamental object in
geometry.
• It is represented by a dot and named by a capital
letter. Point C
• A point represents position only; it has zero size
(that is, zero length, zero width, and zero height).
Lines
l
l
Types of Points
• Points that lie on the same
line are called collinear
points.
• If there is no line on which all
of the points lie, then they
are non-collinear points.
Collinear points M,A, and N
Non-collinear points T, I, and C
Types of Lines
• PARALLEL LINES- two lines that are always the
same distance apart, and will never intersect.
• Parallel can be abbreviated as //.
• An example of parallel lines is on the Italian
flag.
– Line a is parallel to line b:
a // b
Types of Lines
• PERPENDICULAR LINES two coplanar lines that
intersect and form angles
measuring exactly 90°.
• If an angle measures 90°,
a square is place where
the lines intersect to
show that it is a right
angle.
• Perpendicular is often
abbreviated as |.
• line a is perpendicular to
line b: a | b.
Types of Lines
• SKEW LINES - two lines that do not intersect, and are
not parallel.
• Skew lines are always non-coplanar.
• An overpass on a highway is an excellent example of
skew lines.
• This only occurs when you consider lines in 3D space.
Plane
• A plane is an infinite set of points forming a
connected flat surface extending infinitely far in
all directions.
• A plane has infinite length, infinite width, and
zero thickness. It is usually represented in
drawings by a four-sided figure.
• A single capital cursive letter is used to denote a
plane.
R
plane R
T
plane T
Relationships to Planes
• COPLANAR – points or objects on the same
plane.
• Points or objects may not be collinear, but if they
lie in the same plane they are coplanar.
• NONCOPLANAR - any number of points not lying
in the same plane.
Line Segment
• A line segment is a "straight" arrangement of
points between two distinct points– endpoints.
• We write the name of a line segment with
endpoints A and B as AB .
• Note how there are no arrow heads on the line
over AB such as when we denote a line or a ray.
B
A
Midpoint and Bisector of a Segment
• MIDPOINT - A point on the line segment that cuts
the segment into two congruent pieces. Slash
marks are used to indicate the congruent pieces.
• BISECTOR OF A SEGMENT - A line, segment, ray,
or plane that intersects the segment at its
midpoint.
Ray
• A ray is a "straight" line that begins at a certain
point and extends forever in one direction.
• The point where the ray begins is known as its
endpoint.
• We write the name of a ray with endpoint A and
passing through a point B as . The endpoint
must be listed first.
A
G
B
H
Angles
• Two rays that share a common endpoint form
an angle.
• The point where the rays intersect is called the
vertex of the angle.
• The two rays are called the sides of the angle.
Angles, Cont.
• We can specify an angle by using a point on
each ray and the vertex.
• The angle below may be specified as ABC or
as CBA
• This angle may also be this written as  B ,
because B is the vertex point to only ONE angle.
Multiple angles with a shared vertex
A
B
D
C
E
There are 4 angles with vertex B, therefore
each angle MUST be named using 3 points
specific to that angle.
Degrees: Measuring Angles
• We indicate
the size of an
angle using
degrees.
• We use a
protractor to
measure an
angle’s
degrees.
Types of Angles
• Acute Angle:
– Measures between 0°
and 90°
• Right Angle:
– Measure of 90°
• Obtuse Angle:
– Measure between 90°
and 180°
Angle Relationships
• Complementary Angles: Two
angles whose sum of their degree
measurements equals 90°.
• Supplementary Angles: Two angles
whose sum of their degree
measurements equals 180°.
Angle Relationships
• Congruent Angles: Angles
with equal measures.
• Adjacent Angles: Share a
vertex and a common side
but no interior points.
• Bisector of an angle: a ray
that divides the angle into
two congruent angles.
OY
Congruent vs Equal
Congruent:
Equal:
• Refers to two numbers (the measures of the segments)
that are equal.
• AB without the bar on top, means the length of the
segment.
Conjectures: Postulates and Theorems
• Postulate: A statement that is accepted without
proof. Usually these have been observed to be
true but cannot be proven using a logic
argument.
• Theorem: A statement that has been proven
using a logic argument.
– Many theorems follow directly from postulates.
• Throughout this textbook Postulates and
Theorems are referred to as Conjectures.
Conjectures Relating
Points, Lines, and Planes
• A line contains at least two points; a plane
contains at least three points not all in one
line; space contains at least four points not all
in one plane.
Conjectures Relating
Points, Lines, and Planes
• Through any two points there is exactly one line.
Conjectures Relating
Points, Lines, and Planes
• Through any three points there is at least one
plane (if collinear), and through any three noncollinear points there is exactly one plane.
Conjectures Relating
Points, Lines, and Planes
• If two points are in a plane, then the line that
contains the points is in that plane.
Conjectures Relating
Points, Lines, and Planes
• If two planes intersect, then their intersection is a
line.
Major Conjectures Relating
Points, Lines, and Planes
• If two lines intersect, then they intersect in exactly
one point.
• Through a line and a point not in the line there is
exactly one plane.
• If two lines intersect, then exactly one plane
contains the lines.
The Measure of…notation
Time to ponder…..
1. Coplanar lines that do not intersect
A. vertical
B. parallel
C. ray
D. plane
2. A an infinite number of points that has two distinct end points
A. bisect
B. line segment
C. intersect
D. congruent
Time to ponder…..
3. Any three or more points that lie in the same plane
A. coplanar
B. line
C. plane
D. collinear
4. Coplanar → Points on the same line
True
False
5. Line → one endpoint and extends indefinitely in one direction
True
False
Time to ponder…..
6. Collinear → an infinite number of points that goes on forever in
both directions
True
False
7. Plane → an infinite number of points that goes on forever in both
directions
True
False
9.
10.
Give another names for plane S.
Name three collinear points.
11. Name the point of intersection of line AC and plane S.
The End
Once you study all the fancy
words/vocabulary, Geometry is very
easy to understand…so STUDY!
You are Learning a new Language.