Geometry Honors · Lesson 1.2

Inductive and Deductive Reasoning

How it works

Induction suggests a pattern from examples. Deduction proves a conclusion from accepted premises. Checking many cases does not prove a claim about every number or every figure.

a=b,\ b=c\ \Rightarrow\ a=c

Worked examples

Example 1

The first three odd-number sums are $\displaystyle 1=1$ , $\displaystyle 1+3=4$ , and $\displaystyle 1+3+5=9$ . What pattern is suggested?

The sum of the first $\displaystyle n$ positive odd numbers appears to be $\displaystyle n^2$ . These examples suggest rather than prove the claim.

Example 2

If all right angles are congruent and angles $\displaystyle A$ and $\displaystyle B$ are right angles, what follows?

Angles $\displaystyle A$ and $\displaystyle B$ are congruent by deduction from the two premises.

Problems

Problem 1.2.1

A sequence starts $\displaystyle 2,4,8$ . Must its next term be $\displaystyle 16$ ?

Show worked solution

No. Doubling suggests $\displaystyle 16$ , but three terms do not uniquely determine a rule.

Problem 1.2.2

Use deduction: $\displaystyle AB=CD$ , $\displaystyle CD=EF$ , and $\displaystyle EF=7$ . Find $\displaystyle AB$ .

Show worked solution

By transitivity, $\displaystyle AB=EF=7$ .

Problem 1.2.3

Disprove: Every prime number is odd.

Show worked solution

The prime number $\displaystyle 2$ is even. One counterexample is enough.

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 1.2.1

Problem 1.2.2

Problem 1.2.3

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