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# Geometry Chapter 2 Test Flashcards

Created by
@AttentiveRococo

### What is a conjecture?

• An educated guess based on known information (correct)
• A visual representation
• A proven theorem
• A false assumption
• ### What is inductive reasoning?

Examining several specific situations to arrive at a conjecture.

congruent

### What is a counterexample?

<p>A false example used to disprove a statement.</p> Signup and view all the answers

### A statement is either true or false but not both.

<p>True</p> Signup and view all the answers

### What does the truth value represent?

<p>The truth or falsity of a statement</p> Signup and view all the answers

### What is a conjunction?

<p>A compound statement formed by joining two or more statements with 'and'.</p> Signup and view all the answers

### A disjunction is true when at least one of the statements is false.

<p>False</p> Signup and view all the answers

### Match the terms with their definitions.

<p>Conditional Statement = A statement written in 'if - then' form Converse = Switching the hypothesis and conclusion Contrapositive = Negating both hypothesis and conclusion and switching them Deductive Reasoning = Reaching logical conclusions using facts, rules, and definitions</p> Signup and view all the answers

### What is the law of syllogism?

<p>It allows one to skip the middle part of two 'if' statements to derive a conclusion.</p> Signup and view all the answers

### What is a biconditional statement?

<p>A statement where both the conditional and its converse are true.</p> Signup and view all the answers

### The equation for a conjecture for right angles is __________.

<p>(AB)^2 + (BC)^2 = (AC)^2</p> Signup and view all the answers

### What is the purpose of a two-column proof?

<p>To organize statements and reasons in two columns, using given information.</p> Signup and view all the answers

## Study Notes

### Vocabulary and Definitions

• Conjecture: An educated guess based on known information, similar to a hypothesis.
• Inductive Reasoning: Involves examining specific cases to formulate a conjecture or pattern.
• Counterexample: A false example used to disprove a conjecture, demonstrating its inaccuracy.
• Statement: A sentence that can be exclusively true or false; examples include P or Q.
• Truth Value: Indicates whether a statement is true (T) or false (F).
• Negation: The opposite meaning and truth value of a statement, represented as p = not p.
• Compound Statement: Formed by joining two or more statements.
• Conjunction: A compound statement that combines statements with "and," denoted as P ^ Q, true only if all statements are true.
• Disjunction: Connects statements with "or," represented as P v Q, true if at least one statement is true.

### Logic and Relationships

• Venn Diagrams: Visually represent conjunctions (intersection) and disjunctions (union).
• Conditional Statement: Structured as "if p, then q," where p is the hypothesis and q is the conclusion.
• Converse: Formed by reversing the hypothesis and conclusion of a conditional statement.
• Inverse: Retains the order of hypothesis and conclusion but negates both.
• Contrapositive: Switches and negates hypothesis and conclusion, logically equivalent to the original conditional.

### Reasoning Techniques

• Deductive Reasoning: Relies on established facts and definitions to draw logical conclusions; useful for proofs.
• Law of Detachment: Derives conclusions from a true conditional statement, ensuring sufficient information is available.
• Law of Syllogism: Connects multiple "if" statements to derive conclusions, eliminating repeated middle parts.
• Two-Column Proof: A structured format that organizes statements and reasons into two columns, facilitating formal proofs.

### Theorems and Properties

• Supplement Theorem: States that angles forming a linear pair are supplementary.
• Complement Theorem: Asserts that adjacent angles whose noncommon sides form a right angle are complementary.
• Postulate/Axiom: Statements accepted as true without proof.

### Special Cases and Examples

• Right Angles Conjecture: This conjecture states that in a right triangle, (AB)² + (BC)² = (AC)², linking the lengths of the triangle's sides.
• Filling Truth Tables: Use patterns to fill rows for statements, ensuring combinations of true and false values are represented appropriately. Negative letters require opposite truth values.

### Practical Application

• Counterexample Presentation: Can be illustrated through diagrams or descriptive explanations.
• Conclusion Writing: Involves summarizing inferences drawn from given logical statements, excluding conjunction or disjunction terms.

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## Description

Test your knowledge of key concepts in Geometry Chapter 2 with these flashcards. Learn important terms like conjecture and inductive reasoning, which are essential for understanding geometric principles and patterns. Perfect for reviewing before a quiz or exam!

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