Key Concepts: Proving Segment Relationships

Properties of Segment Congruence

• Reflexive: AB ≅ AB
• Symmetric: If AB ≅ CD, then CD ≅ AB
• Transitive: If AB ≅ CD and CD ≅ EF, then AB ≅ EF

Two-Column Proof

A two-column proof organizes statements and reasons side by side:

• Left column: Statements (what is true)
• Right column: Reasons (why it is true — definitions, postulates, theorems, properties)

Segment Addition Postulate in Proofs

The Segment Addition Postulate (If B is between A and C, then AB + BC = AC) is frequently used to prove segment relationships.