Geometry Chapter 2 Test Flashcards

Questions and Answers

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.

The opposite sides of a geometric figure are __________ if the midpoint is given.

congruent

What is a counterexample?

A false example used to disprove a statement. Signup and view all the answers

A statement is either true or false but not both.

True Signup and view all the answers

What does the truth value represent?

The truth or falsity of a statement Signup and view all the answers

What is a conjunction?

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

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

False Signup and view all the answers

Match the terms with their definitions.

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 Signup and view all the answers

What is the law of syllogism?

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

What is a biconditional statement?

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

The equation for a conjecture for right angles is __________.

(AB)^2 + (BC)^2 = (AC)^2 Signup and view all the answers

What is the purpose of a two-column proof?

To organize statements and reasons in two columns, using given information. 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.

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!