Postulates, Theorems, and
Proofs
Goals:
· Properly use postulates and theorems
· Know the kinds of reasons that can be
used in proofs
Postulate vs. Theorem
Reasons used in Proofs:
Midpoint Theorem
If M is the midpoint of
Draw a picture:
Now let's prove why it is true!
Given: M is the midpoint of
Prove:
Angle Bisector Theorem
If BX is the bisector of
Draw a picture:
Now let's prove why it is true!!!
Given:
Prove:
then
Theorems
· If two lines intersect, then they intersect in exactly one point.
· Through a line and a point not on the line there is exactly one
plane.
· If two lines intersect, then exactly one plane contains the lines.
Postulates
· Through any two points there is exactly one line.
· If two points are in a plane, then the line that contains the points is
in that plane
· If two planes intersect, then their intersection is a line.
· Through any three points there is at least one plane, and through any
three noncollinear points there is exactly one plane.
· 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.
P/T/P
Grade: 10
Subject: Honors Geometry
Date: «date»
1
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
2 AE + EF = AF
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
3
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
4
A
Definition of Midpoint
B
Defintion of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
5
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
6
A
Definiton of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
7
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
8
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
9
A
Definition of Midpoint
B
Definition of Angle Bisector
C
Angle Addition Postulate
D
Segment Addition Postulate
E
Midpoint Theorem
F
Angle Bisector Theorem
G
Definition of Segment Bisector
Homework
· Compare and contrast the Definition of Midpoint and the
Midpoint Theorem (1-2 paragraphs)
·
· Complete the following proof.