In this unit you will extend your knowledge of a logical procedure for verifying
geometric relationships. You will analyze conjectures and verify conclusions. You will
use definitions, properties, postulates, and theorems to verify steps in proofs. The proofs
in this lesson will focus on segment and angle relationships.
Addition Properties
Subtraction Properties
Multiplication and Division Properties
Proofs
Addition Properties
Two-column proof – A two column proof is an organized method that shows
statements and reasons to support geometric statements about a theorem.
Let’s take a close look at the two-column proof of this theorem. In a two-column proof,
both the “given” and “conclusion” are stated at the beginning, a diagram may be drawn as
a visual aid, and then statements and their corresponding reasons are listed.
Given:
Conclusion:
Statement Reason
1. MP ST ≅ 1. Given
2. MP ST = 2. Definition of Congruence
3. MP PS ST PS +=+ 3. Addition Property of Equality
4. MP PS MS + = ; ST PS PT + = 4. Segment Addition (Postulate 2-B)
5. MS PT = 5. Substitution Property of Equality
6. MS PT ≅ 6. Definition of Congruence (Remember:
definitions are reversible)