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Questions and Answers
What is an educated guess based on known information?
What is an educated guess based on known information?
Conjecture
What is an example used to show that a given statement is not always true?
What is an example used to show that a given statement is not always true?
Counterexample
What type of statement can be written in if-then form?
What type of statement can be written in if-then form?
Conditional statement
What is the form if p, then q referred to as?
What is the form if p, then q referred to as?
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What is the phrase that follows the word if in a conditional statement?
What is the phrase that follows the word if in a conditional statement?
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What is the phrase that follows the word then in a conditional statement?
What is the phrase that follows the word then in a conditional statement?
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What reasoning uses facts, definitions, or properties to reach logical conclusions?
What reasoning uses facts, definitions, or properties to reach logical conclusions?
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What is a statement that is accepted as true without proof called?
What is a statement that is accepted as true without proof called?
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What is a paragraph written to explain why a conjecture for a given situation is true called?
What is a paragraph written to explain why a conjecture for a given situation is true called?
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What contains statements and reasons organized in two columns to prove conjectures and theorems?
What contains statements and reasons organized in two columns to prove conjectures and theorems?
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What property is represented by ∠1≅∠1?
What property is represented by ∠1≅∠1?
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What theorem states that if ∠1≅∠2, then ∠2≅∠1?
What theorem states that if ∠1≅∠2, then ∠2≅∠1?
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What theorem asserts that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?
What theorem asserts that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?
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Examining several specific situations to arrive at a conjecture (prediction or plausible generalization) is called _____.
Examining several specific situations to arrive at a conjecture (prediction or plausible generalization) is called _____.
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What is represented by (AB) ̅≅(AB) ̅?
What is represented by (AB) ̅≅(AB) ̅?
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What theorem states that if (AB) ̅≅(CD) ̅, then (CD) ̅≅(AB) ̅?
What theorem states that if (AB) ̅≅(CD) ̅, then (CD) ̅≅(AB) ̅?
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What theorem asserts that if (AB) ̅≅(CD) ̅ and (CD) ̅≅(EF), then (AB) ̅≅(EF) ̅?
What theorem asserts that if (AB) ̅≅(CD) ̅ and (CD) ̅≅(EF), then (AB) ̅≅(EF) ̅?
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What are the five parts of a good proof?
What are the five parts of a good proof?
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What theorem states that if ∠1≅∠2, then ∠2≅∠1?
What theorem states that if ∠1≅∠2, then ∠2≅∠1?
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What theorem states that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?
What theorem states that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?
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If two angles form a linear pair, what can be said about them?
If two angles form a linear pair, what can be said about them?
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If the noncommon sides of two adjacent angles form a right angle, what can be said about them?
If the noncommon sides of two adjacent angles form a right angle, what can be said about them?
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What is a statement?
What is a statement?
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What refers to the truth or falsity of a statement?
What refers to the truth or falsity of a statement?
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What is the opposite meaning and opposite truth value called?
What is the opposite meaning and opposite truth value called?
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What is a compound statement?
What is a compound statement?
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What is a conjunction?
What is a conjunction?
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What is a disjunction?
What is a disjunction?
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What is a convenient method for organizing the truth values of statements?
What is a convenient method for organizing the truth values of statements?
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What is it called when exchanging the hypothesis and conclusion of the conditional?
What is it called when exchanging the hypothesis and conclusion of the conditional?
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What is the inverse of a conditional statement?
What is the inverse of a conditional statement?
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What is the contrapositive of a conditional statement?
What is the contrapositive of a conditional statement?
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What is a biconditional statement?
What is a biconditional statement?
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What is the Law of Detachment?
What is the Law of Detachment?
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What is the Law of Syllogism?
What is the Law of Syllogism?
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Through any two points there is _____
Through any two points there is _____
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Through any three points not on the same line there is _____
Through any three points not on the same line there is _____
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A line contains at least _____
A line contains at least _____
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If two planes intersect, then _____
If two planes intersect, then _____
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Two lines intersect at _______
Two lines intersect at _______
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What does the midpoint theorem state?
What does the midpoint theorem state?
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If two angles are vertical angles, what can be said about them?
If two angles are vertical angles, what can be said about them?
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Study Notes
Key Definitions in Geometry
- Conjecture: An educated guess based on known information.
- Counterexample: An example demonstrating that a statement is not always true.
- Conditional Statement: A statement expressed in "if-then" form, such as "if two angles have the same measure, then they are congruent."
- If-Then Statement: A specific type of conditional statement detailing the hypothesis and conclusion.
Components of Conditional Statements
- Hypothesis: The part that follows "if" in a conditional statement, symbolized as p.
- Conclusion: The part that follows "then" in a conditional statement, symbolized as q.
Logical Reasoning
- Deductive Reasoning: Using facts and definitions to draw logical conclusions from given statements.
- Inductive Reasoning: Arriving at a conjecture through the examination of several specific situations.
Types of Proof
- Paragraph Proof: A written explanation supporting why a conjecture is true, often informal.
- Two-Column Proof: Organized statements and reasons arranged in two columns to prove conjectures and theorems.
Properties of Congruence
- Reflexive Property of Angle Congruence: ∠1 ≅ ∠1.
- Symmetric Property of Angle Congruence: If ∠1 ≅ ∠2, then ∠2 ≅ ∠1.
- Transitive Property of Angle Congruence: If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.
Additional Properties for Segments
- Reflexive Property of Segment Congruence: (AB)̅ ≅ (AB)̅.
- Symmetric Property of Segment Congruence: If (AB)̅ ≅ (CD)̅, then (CD)̅ ≅ (AB)̅.
- Transitive Property of Segment Congruence: If (AB)̅ ≅ (CD)̅ and (CD)̅ ≅ (EF)̅, then (AB)̅ ≅ (EF)̅.
Important Theorems
- Supplement Theorem: Angles that form a linear pair are supplementary.
- Complement Theorem: Adjacent angles with noncommon sides forming a right angle are complementary.
Statements and Truth Values
- Statement: A sentence that can be classified as either true or false.
- Truth Value: Indicates the truth or falsity of a statement.
- Negation: The opposite of a statement, symbolized as ~p.
Compound Statements
- Compound Statement: Multiple statements joined by "and."
- Conjunction: A compound statement formed using "and," symbolized as p ^ q.
- Disjunction: A compound statement formed using "or," symbolized as p ˅ q; true if at least one statement is true.
Truth Tables
- Truth Table: A systematic way to organize the truth values of statements.
Conditional Logic Transformations
- Converse: Exchanging the hypothesis and conclusion of a conditional statement.
- Inverse: Negating both the hypothesis and conclusion of the conditional statement.
- Contrapositive: Negating both the hypothesis and conclusion of the converse statement.
- Biconditional: The conjunction of a conditional and its converse, denoted as (p ↔ q).
Laws of Logic
- Law of Detachment: If p → q is true and p is true, then q is true.
- Law of Syllogism: If p → q and q → r are true, then p → r is true.
Geometric Principles
- A unique line exists through any two points.
- A unique plane exists through any three non-collinear points.
- A line contains at least two points.
- The intersection of two planes is a line.
- Two lines intersect at exactly one point.
Midpoint and Congruency
- Midpoint Theorem: If M is the midpoint of AB, then AM ≅ MB.
- Vertical Angle Theorem: Vertical angles are always congruent.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with flashcards from Glencoe Geometry Chapter 2. This quiz covers essential concepts such as conjectures, counterexamples, and conditional statements in geometry. Perfect for reinforcing your understanding of the chapter's key terms.
