Download 1-2 Points, Lines and Planes

Points, Lines and Planes
Overview
What you should already
know!
What you should learn!
• Point - no size, location; represented
by a small dot and named by a capital
letter; A.
• A geometric figure is a set of points.
• Space is the set of all points.
S
X
A
C
B
Q
• Line - series of points that extends in two
opposite directions. Name with two points,
AB, or a lower case letter, l.
A
B
l
•Points that lie on the same
line are collinear.
•Name 3 collinear points.
•Name 3 non-collinear
points.
Plane - flat surface that extends in all
directions; it has no thickness. Name a
plane with a single capital letter, P, or
name at least 3 non-collinear points in the
plane.
Points and lines
in the same
plane are
coplanar.
1. Name this plane in two ways.
2. Can plane Q be called plane
ABF?
plane ABD?
3. Are the following points
collinear?
A, B, C
E, B, C
4. Are the following sets of
points coplanar?
Plane Q and line BF
line AB and line ED
Euclid of
Alexandria
Born: about 325 BC
Died: about 265 BC in
Alexandria, Egypt
“Father of Geometry”
Wrote the “Book of
Elements” - set of 13 books
with definitions, postulates,
axioms, and theorems
A postulate or axiom is an
accepted fact.
Postulate 1-1
Through any two points there is
exactly one line
A
B
l
Postulate 1-2
If two lines intersect, then they
intersect in exactly one point.
C
B
A
E
D
Postulate 1-3
If two planes intersect, then they
intersect in exactly one line.
Postulate 1-4
Through any three noncollinear
points there is exactly one plane.
S
X
B
C
Q
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