Transcript 1.5 Postulates and Theorems

Geometry
1.5 Postulates and
Theorems Relating Points
& Lines
Some Important Terms
 Postulate(Post.)-a
basic assumption
without proof
 Theorem(Thm.)-a statement that can
be proved using postulates, defn.’s &
previously proved thms.
 Determine-to define or specify
“4 walls, a ceiling, and a floor determine a room”
Some Important Terms
 Exists-there
is at least one
“chairs exist in this room”
 Unique-there
is no more than one
“In this room, the computer is unique, the chairs are not”
 One
and only one-exactly one;
shows existence and uniqueness
“In this room, there is one and only one fire extinguisher”
Postulate 6(Know the meaning not the number)
 Through
any two points there is
exactly one line.
 How
would you write this using the
word determine?
Two points determine a line.
A
B
.
.
Postulate 7(Know the meaning not the number)

Through any three noncollinear points
there is exactly one plane.
.B
.A
.C

Through any three points there is at least
one plane.
See diagram on the board.
Postulate 8(Know the meaning not the number)

If two points are in a plane, then the line
that contains the points is in the plane.
A
.
B
.
Postulate 9(Know the meaning not the number)
 If
two planes intersect, then their
intersection is a line.
B
A
.
.
Theorem 1.1 (Know the meaning not the number)

If two lines intersect, then they intersect
in exactly one(one and only one) point.
A
.
The point exists(there is at least one point) and is
unique(no more than one point exists).
Theorem 1.2 (Know the meaning not the number)

Through a line and a point not in the line, there is
exactly one(one and only one) plane.
The plane exists(there is at least one plane) and is unique(no more
than one plane exists).
A
.
Theorem 1.3 (Know the meaning not the number)

If two lines intersect, then exactly one
and only one) plane contains the lines.
(one
The plane exists(there is at least one plane) and is unique(no more than one
plane exists).
Quick Quiz
 Two
points must be ___________
Collinear
 Three points may be __________
Collinear
 Three points must be __________
Coplanar
 Four points may be __________
Coplanar
Quick Quiz
Three noncollinear points determine a ___
Plane
 A line and a point not on a line determine
a __________
Plane
 A line and a plane can 1)__________
2)_________ or 3)____________
Be Parallel, Intersect in exactly one point, or
the plane can contain the line
 Four noncoplanar points determine
__________
Space

Homework
 P.
21 #4-32(4X)
P. 25 #1-17 Odd
P. 29 S.T. #1-11 Odd
 Bring Compass Tomorrow