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. - презентация

1 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.

2 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. =

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

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

5 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.

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