2.7.notebook
October 19, 2010
Proving Segment Relationships
• We will learn some postulates and theorems describing basic segment relationships.
• We will use those postulates and theorems to write some basic proofs of segment relationships.
Postulates and Theorems:
Postulate 2.8 (Ruler Postulate) ­ in your book.
Postulate 2.9 (Segment Addition Postulate) ­ If B is between A and C, then AB + BC = AC.
Theorem 2.2 (Segment Congruence) ­ The Reflexive, Symmetric, and Transitive Properties of Equality hold true for congruent segments as well.
If Reflexive
, then
Symmetric
If
and
, then
Transitive
1
2.7.notebook
October 19, 2010
Using the Segment Addition Postulate:
P
Given: PQ = RS
Prove: PR = QS
statements
Q
R S
reasons
Proving the Transitive Property of Congruence:
statements
Given:
Prove:
N
reasons
P
M
Q
R
S
2
2.7.notebook
October 19, 2010
Proof with Segment Congruence:
K
J
statements
L
reasons
H
G
Given:
Prove:
Assignment Questions (p. 103, 12­24 even)
3