1.6Algebraic Proofs
Quick Answer
An algebraic proof uses properties of equality (Addition, Subtraction, Multiplication, Division, Substitution, Distributive) as reasons. Each step must be justified. This is the foundation for geometric proof.
Essential Question
How do algebraic properties of equality serve as the model for the structure of a two-column geometric proof?
Learning Goals
- 1State the properties of equality.
- 2Write two-column algebraic proofs.
- 3Justify each step with a property name.
- 4Identify the structure: statements in the left column, reasons in the right.
Key Vocabulary
Two-column proof
A proof organized with numbered statements on the left and corresponding reasons on the right.
Properties of equality
Rules such as Addition, Subtraction, Multiplication, Division, Substitution, and Distributive properties used to justify steps.
Reflexive Property
a = a; any quantity equals itself.
Symmetric Property
If a = b, then b = a.
Transitive Property
If a = b and b = c, then a = c.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.