Unit 2: Reasoning and Proof · ~15–30 min
Justify each step of an equation-solving or geometric proof using the properties of equality and the properties of congruence.
These are the algebra rules you've used for years — now with formal names you'll cite as reasons in a proof.
| Property | Meaning |
|---|---|
| Addition | If a=b, then a+c=b+c |
| Subtraction | If a=b, then a−c=b−c |
| Multiplication | If a=b, then ac=bc |
| Division | If a=b and c≠0, then a÷c=b÷c |
| Substitution | If a=b, then a can replace b in any expression |
| Distributive | a(b+c)=ab+ac |
| Reflexive | a=a |
| Symmetric | If a=b, then b=a |
| Transitive | If a=b and b=c, then a=c |
Segments, angles, and other figures have their own parallel set: the Reflexive, Symmetric, and Transitive Properties of Congruence. They work exactly like their equality counterparts, just applied to congruence (≅) instead of equality (=) — for example, segment AB ≅ segment AB is true by the Reflexive Property of Congruence.
Segment Addition Postulate: if C is between A and B, then AC + CB = AB.