1. Proving Segment Relationships
Chapter 2.7
Proving Segment Relationships
Objective: Practice using proofs for geometric relationships by starting with segments
Spi.1.4
Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems.
Check.4.3
Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs

2. If AB  CD, and CD  EF, then AB  EF
Geometric Properties
Add to your
listing
Postulate 2.8 (Ruler Postulate)
The points on any line or line segment can be paired with real numbers so that given any two points A and B on a line, A corresponds to zeros and B corresponds to a positive real number.
Postulate 2.9 (Segment Addition Postulate)
If B is between A and C, then AB + BC = AC or
If AB + BC = AC, then B is between A and C
Theorem 2.2
Congruence of segments is reflexive, symmetric, and transitive. AB BC A B C AC
Reflexive Property
AB  AB
Symmetric Property
If AB  CD, then CD  AB
Transitive Property
If AB  CD, and CD  EF, then AB  EF
It's not what you look at that matters, it's what you see. Henry David Thoreau

3. Use paper to solve Given BC = DE Prove AB + DE = AC Statements Reasons
AB + BC = AC
AB + DE = AC
Given
Segment Addition Postulate
Substitution

4. Use paper to solve Given PR  QS Prove PQ  RS Statements Reasons
PQ + QR = PR
QR + RS = QS
PQ + QR = QR + RS
PQ = RS
PQ  RS
Given
Definition of Congruence
Segment Addition Postulate
Substitution
Subtraction

5. Proof with Segment Addition process
Prove the following:
Given: PQ = RS
Prove: PR = QS P Q R S
Statements
Reasons
PQ = RS
PQ + QR = QR + RS
PQ + QR = PR and QR + RS = QS
PR = QS
Given
Addition Property
Segment Addition Postulate
Substitution

6. Proof with Segment Addition process
Prove the following:
Given: PR = QS
Prove: PQ = RS P Q R S
Statements
Reasons
PR = QS
PR - QR = QS - QR
PR - QR = PQ and QS - QR = RS
PQ = RS
Given
Subtraction Property
Segment Addition Postulate
Substitution

7. Proof with Segment Congruence processJ
Prove the following:
Given: JK  KL, HJ  GH, KL  HJ
Prove: GH  JK K L
Statements
Reasons H G
JK  KL, KL  HJ
JK  HJ
HJ  GH
JK  GH
GH  JK
Given
Transitive Property
Symmetric Property

8. Given: AC = AB AB = BX CY = XD Prove: AY = BD
Prove the following.
Given: AC = AB AB = BX CY = XD Prove: AY = BD
1. Given
AC = AB, AB = BX 1.
2. Transitive Property
AC = BX 2.
3. Given
CY = XD 3.
4. Addition Property
AC + CY = BX + XD 4.
AY = BD
6. Substitution 6.
Proof:
Statements Reasons
Which reason correctly completes the proof?
5. ________________
AC + CY = AY; BX + XD = BD 5. ?
Segment Addition Postulate

9. Practice Assignment
Page 145, even