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Section ____________________ Vocabulary Date__________ Prove Statements about Segments and Angles Definition Example Statements PROOF TWO-COLUMN PROOF THEOREM CONGRUENCE of SEGMENTS CONGRUENCE of ANGLES A proof is a logical argument that shows a statement is true. A two-column proof has numbered statements and corresponding reasons that show an argument in logical order. example A theorem is a statement that can be proven. Reflexive For any segment ̅̅̅̅ AB, ____ ≅ ____ Symmetric If ̅̅̅̅ AB ≅ ̅̅̅̅ CD ,then ____ ≅ ____ Transitive ̅̅̅̅, then ____ ≅ ____ If ̅̅̅̅ AB ≅ ̅̅̅̅ CD and ̅̅̅̅ CD ≅ EF Reflexive For any angle A, ____ ≅ ____ Symmetric If ‹A ≅ ‹B, then ____ ≅ ____ Transitive If ‹A ≅ ‹B and ‹B ≅ ‹C, then ____ ≅ ____ Reasons 1. 2. 3. 4. 5. 1. GIVEN 2. 3. 4. 5. * the last statement is ALWAYS what you are trying to prove * the first reason(s) is ALWAYS your GIVEN(s)