Reasoning and Proof

### Overview

The first half of the chapter focuses on logic, including inductive and deductive reasoning and the differences between them. Statements, truth tables, and related terminology are also introduced. The second half of the chapter introduces students to creating two-column proofs, both algebraic and geometric, providing a foundation for the development of proofs in later chapters.

### What you can expect to learn

After completing these activities you should be able to

1. Identify inductive and deductive reasoning and their role in
mathematics.
2. Make conjectures and use counterexamples.
3. Recognize typical fallacies in inductive and deductive reasoning.
4. Define and determine the truth value of simple and compound statements (negation, conjunction, disjunction, conditional, converse, inverse, contrapositive, and biconditional).
5. Identify truth values using truth tables.
6. Evaluate the truth, validity, and soundness of deductive arguments.
7. Identify key subsets and properties of the real numbers.
8. Prove and apply theorems involving segments, lines, angles, and bisectors.
9. Construct perpendicular bisectors of segments and angle bisectors.
10. Recognize that our designs often imitate those in God’s creation.
Activity List