Prentice Hall Geometry

Chapter 2 Reasoning and Proof > 2 Chapter Review

2 Chapter Review

Connecting BIG ideas and Answering the Essential Questions

Reasoning and Proof

You can observe patterns to make a conjecture; you can prove it is true using given information, definitions, properties, postulates, and theorems.

Inductive Reasoning (Lesson 2-1)

Inductive reasoning is the process of making conjectures based on patterns.

From 3 to 9 is times 3. From 9 to 27 is times 3. From 27 to 81 is times 3.

Proofs (Lessons 2-5 and 2-6)

A two-column proof lists the statements to the left and the corresponding reasons to the right. In a paragraph proof, the statements and reasons are written as sentences.

Statements	Reasons
given information information from a diagram logical reasoning statement to prove	definitions properties postulates previously proven theorems

Deductive Reasoning (Lessons 2-2, 2-3, 2-4)
Deductive reasoning is the process of making logical conclusions from given statements or facts.

Law of Detachment			Law of Syllogism
If	p rightwards arrow q	is true	If	p rightwards arrow q	is true
and	p	is true,	and	q rightwards arrow r	is true,
then	q	is true.	then	p rightwards arrow r	is true.

Chapter Vocabulary

biconditional (p. 98)
conclusion (p. 89)
conditional (p. 89)
conjecture (p. 83)
contrapositive (p. 91)
converse (p. 91)
counterexample (p. 84)
deductive reasoning (p. 106)
equivalent statements (p. 91)
hypothesis (p. 89)
inductive reasoning (p. 82)
inverse (p. 91)
Law of Detachment (p. 106)
Law of Syllogism (p. 108)
negation (p. 91)
paragraph proof (p. 122)
proof (p. 115)
theorem (p. 120)
truth value (p. 90)
two-column proof (p. 115)

Choose the correct vocabulary term to complete each sentence.

The part of a conditional that follows “then” is the modified question mark with under bar below , .
Reasoning logically from given statements to a conclusion is modified question mark with under bar below , .
A conditional has a(n) modified question mark with under bar below of true or false.
The modified question mark with under bar below of a conditional switches the hypothesis and conclusion.
When a conditional and its converse are true, you can write them as a single true statement called a(n) modified question mark with under bar below , .
A statement that you prove true is a(n) modified question mark with under bar below , .
The part of a conditional that follows “if” is the modified question mark with under bar below , .

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2 Chapter Review

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