Points, Lines,
and Planes
Sections 1.1 & 1.2
Notecard 1
Definition of a Point
A point has no dimension.
It is represented by a dot.
A point is symbolized using an upper-case
letter.
Notecard 2
Definition: Line
A line has one dimension. (infinite length)
A line is named using any two points on the
line with a two sided arrow above them like
this: 𝐴𝐵. It can also be named by using a
lower-case cursive letter.
Through any two points, there is exactly one
line.
Notecard 3
Definition: Collinear points
points that lie on the same line.
Notecard 4
Definition: Between
If a point is between two other points then
that means it must also be collinear with the
other two points.
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Definition: Plane
A plane has two dimensions. It is represented
by a shape that looks like a floor or a wall, but it
extends infinitely in length and width.
Any three non-collinear points can define a
plane.
A plane is named using the word plane with 3
non-collinear points or with an upper-case
cursive letter.
Notecard 6
Definition: Coplanar:
Coplanar points are points that lie (or could
lie) in the same plane.
Notecard 7
Definition: Line Segment:
The line segment consists of two endpoints
and all the points between them.
A line segment is named using both
endpoints with a line above them like this:
𝐴𝐵.
𝐴𝐵 and 𝐵𝐴 refer to the same line segment.
Notecard 8
Definition: Ray
The ray consists of an endpoint and all points on
a line in the opposite direction.
A ray is named using its endpoint first and then
any other point on the ray with a ray symbol
pointing to the right above them like this: 𝐴𝐵.
𝐴𝐵 and 𝐵𝐴 do not refer to the same ray.
Notecard 9
Definition: Opposite Rays:
If point C lies on line AB between A and B,
then ray CA and ray CB are opposite rays.
Two opposite rays make a line.
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Definition: Intersection:
The intersection of two or more figures is the
set of points the figures have in common.
The intersection of 2 different lines is a point.
The intersection of 2 different planes is a
line.
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Definition: Distance:
The distance between points A and B, also
known as the length of line segment AB is
the absolute value of the difference of the
coordinates of A and B. In other words,
distance is many units apart the points lie.
The distance from A to B, or the length of 𝐴𝐵
Is written as AB. (No symbol above).
Notecard 12
Definitions:
Postulate: A rule that is accepted without
proof.
Theorem: A rule that can be proven.
Notecard 13
The Ruler Postulate:
The points on a line can be matched one to
one with the real numbers.
Notecard 14
Segment Addition Postulate:
If B is between A and C, then AB + BC = AC.
If AB + BC = AC, then B is between A and C.
Notecard 15
Definition: Congruent Segments:
Line segments that equal (=) length are
called congruent (≅)segments.
To show that two segments are congruent in a
drawing we use tick marks.
A
B
C
D