1. 2.6 Proofs September 13, 2011
2.6 Prove Statements about Segments & Angles
Proof: logical argument that shows a statement is True.
2‐column proof: numbered statements and corresponding reasons that
show an argument in logical order
Example 1
HW pg. 116 #3­12, 16­18, 29 1

2. 2.6 Proofs September 13, 2011
Writing a 2‐column proof
• Organize reasoning by drawing the diagram
• Make 1 statement @ a time.
• Start with the given
• End with the conclusion(prove part)
Example 1
HW pg. 116 #3­12, 16­18, 29 2

3. 2.6 Proofs September 13, 2011
Theorem: statement that can be proven
Theorem 2.1 : Congruence of Segments
Reflexive: AB ≅ AB
Symmetric: If AB ≅ CD, then CD ≅ AB
Transitive: If AB ≅ CD & CD ≅ EF, then AB ≅ EF
Theorem 2.2 : Congruence of Angles
Reflexive: <A ≅ <A
Symmetric: If <A ≅ <B, then <B ≅ <A
Transitive: If <A ≅ <B & <B ≅ <C, then <A ≅ <C
Example 2
HW pg. 116 #3­12, 16­18, 29 3

4. 2.6 Proofs September 13, 2011
Example 3
HW pg. 116 #3­12, 16­18, 29 4

5. 2.6 Proofs September 13, 2011
HW pg. 116 #3­12, 16­18, 29 5

6. 2.6 Proofs September 13, 2011
HW pg. 116 #3‐12, 16‐18, 29
HW pg. 116 #3­12, 16­18, 29 6