Page 197 - Math Course 2 (Book 2)

Proving Segment Relationships
Mo. 12

Lesson 7 THEOREM 12.2

Segment Congruence

KEY CONCEPTS:
Congruence of segments is reflexive, symmetric,
1. Write proofs involving segment addition. and transitive.
2. Write proofs involving segment congruence
Reflexive
Property AB ≅ AB

Symmetric
Property If AB ≅ CD, then CD ≅ AB.
MO. 12 - L7a
Transitive If AB ≅ CD, and CD ≅ EF, then
Proving Segment Addition and Property AB ≅ EF.

Segment Congruence B C

A D
POSTULATES E F

Ruler Postulate

12.8 The points on any line or line segment can
be paired with real numbers so that, give Let’s Begin
any two points A and B on a line, A corre-
sponds to zero, and B corresponds to a
positive real number.
A B
Proof with Segment Addition

Example
0

Segment Addition Postulate Prove the following.
Given: PS = QS
12.9 If A, B, and C are collinear and B is between Prove: PQ = RS P Q R S
A and C, then AB + BC = AC. Proof:
Statements Reasons
If AB + BC = AC, then B is between A and C.
1. PR = QS 1. Given

AB BC 2. PR – QR = QS – QR 2. Subtraction Property
A B C 3. PR – QR = PQ; 3. Segment Addition
QS – QR = RS Postulate
AC 4. PQ = RS 4. Substitution

189