Sec. 2.6: Proofs Using Segments and Angles A proof is a logical argument that shows a statement is true. In a two-column proof the statements are in the.

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Sec. 2.6: Proofs Using Segments and Angles A proof is a logical argument that shows a statement is true. In a two-column proof the statements are in the left column and the reasons are in the right.

Example Given: AB + AB = AC Prove: AB = BC StatementsReasons 1.AB + AB = AC1. Given 2.AC = AB + BC2. Seg. Add. Post. 3.AB + AB = AB + BC3. Subst. Prop. = 4.AB = BC4. Subtraction Prop. =

Definition of Congruence for Segments Note: Definitions are biconditional. Two segments are congruent if and only if they have the same measure. i.e.

Definition of Congruence for Angles Two angles are congruent if and only if they have the same measure. i.e.

A theorem is a statement that can be proven. Once you have proven a theorem, you can use the theorem as a reason in other proofs.

Given Substitution Prop. = Definition of Congruent Segments Transitive Prop. = Definition of Congruent Segments