Transcript 1-2 Points, Lines, and Planes Continued

1-2
Points, Lines,
and Planes
Undefined Terms
Term Description
Point: indicates a location
and has no size
How to Name it
Diagram
Point A
OR
∙𝐴
A
Line: represented by a
straight path that extends in
two opposite directions
without end and has no
thickness. A line contains
infinitely many points
Name a line by any two
points on the line: 𝐴𝐵 or 𝐵𝐴
Plane: represents a flat
surface that extends without
end and has no thickness. A
plane contains infinitely many
lines
Name a plane by a capital
letter, such as plane P
B
Or by a single lowercase
letter such as line m
Or by at least three points in
the plane that do not lie on
the same line, such as plane
ABC
m
A
B
A
P
C
Collinear Points: Points that lie on the
same line
Coplanar: Points and lines that lie in the
same plane
All points of a line are coplanar!
Problem 1: Naming Points, Lines, and Planes
Defined Terms
Term Description
How to Name it
Segment: part of a line that
consists of two endpoints and
all the points between them
Name a segment by its two
endpoints: 𝐴𝐵 or 𝐵𝐴
Ray: part of a line that
consists of one endpoint and
all the points of the line on
one side of the endpoint
Name a ray by its endpoint
and another point on the
ray: 𝐴𝐵 (read “ray AB”). The
order of the points indicates
the ray’s direction
Opposite Rays: two rays that Name opposite rays by their
share the same endpoint and shared endpoint and any
form a line
other point on each ray:
𝐶𝐴 𝑎𝑛𝑑 𝐶𝐵
Diagram
B
A
B
A
B
C
A
Problem 2: Naming Segments and Rays
• What are the names of the segments?
• What are the names of the rays?
• Which of the rays are opposite rays?
• Are 𝐸𝐹 𝑎𝑛𝑑 𝐹𝐸 opposite rays?
DAY 2:
Points, Lines, and
Planes Continued
Problem 3: Finding the
intersections of Two Planes
Postulate (axiom): an accepted
statement of fact. They are
basic building blocks of the
logical system in geometry (to
prove general concepts)
Side note: when you know
two points that two planes
have in common, Postulate
1-1 and 1-3 tell you that the
line through those points is
the intersection of the
planes.
Each surface of the box represents part
of a plane. What is the intersection of
plane ADC and plane BFG?
When you name a plane
from a figure like this box,
list the corner points in
consecutive order. EX:
plane ABCD and plane
ADCB are names for the
top plane but plane ACBD
is not!!
• What are the names of the two planes that
intersect in 𝐵𝐹?
• Why do you only need to find two common
points to name the intersection of two distinct
planes?
Problem 4: Using Postulate 1-4
• What plane contains points N, P,
and Q? Shade the region.
• What plane contains points J, M
and Q? Shade the region.
• What plane contains points L, M
and N? Shade the region.
• What is the name of a line that is
coplanar with 𝐽𝐾 𝑎𝑛𝑑 𝐾𝐿?