Glencoe Geometry Chapter 2 Quiz

Questions and Answers

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?

Counterexample

What type of statement can be written in if-then form?

Conditional statement

What is the form if p, then q referred to as?

If-then statement Signup and view all the answers

What is the phrase that follows the word if in a conditional statement?

Hypothesis Signup and view all the answers

What is the phrase that follows the word then in a conditional statement?

Conclusion Signup and view all the answers

What reasoning uses facts, definitions, or properties to reach logical conclusions?

Deductive reasoning Signup and view all the answers

What is a statement that is accepted as true without proof called?

Postulate or axiom Signup and view all the answers

What is a paragraph written to explain why a conjecture for a given situation is true called?

Paragraph proof Signup and view all the answers

What contains statements and reasons organized in two columns to prove conjectures and theorems?

Two-column proof Signup and view all the answers

What property is represented by ∠1≅∠1?

Reflexive property of angle congruence Signup and view all the answers

What theorem states that if ∠1≅∠2, then ∠2≅∠1?

Symmetric property of angle congruence Signup and view all the answers

What theorem asserts that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?

Transitive property of angle congruence Signup and view all the answers

Examining several specific situations to arrive at a conjecture (prediction or plausible generalization) is called _____.

Inductive reasoning Signup and view all the answers

What is represented by (AB) ̅≅(AB) ̅?

Reflexive property of segment congruence Signup and view all the answers

What theorem states that if (AB) ̅≅(CD) ̅, then (CD) ̅≅(AB) ̅?

Symmetric property of segment congruence Signup and view all the answers

What theorem asserts that if (AB) ̅≅(CD) ̅ and (CD) ̅≅(EF), then (AB) ̅≅(EF) ̅?

Transitive property of segment congruence Signup and view all the answers

What are the five parts of a good proof?

<ol> <li>State the theorem or conjecture to be proven 2. List the given information 3. If possible, draw a diagram 4. State what is to be proved 5. Develop a system of deductive reasoning</li> </ol> Signup and view all the answers

What theorem states that if ∠1≅∠2, then ∠2≅∠1?

Symmetric property of congruence Signup and view all the answers

What theorem states that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?

Transitive property of congruence Signup and view all the answers

If two angles form a linear pair, what can be said about them?

They are supplementary angles. Signup and view all the answers

If the noncommon sides of two adjacent angles form a right angle, what can be said about them?

They are complementary angles. Signup and view all the answers

What is a statement?

Any sentence that is either true or false, but not both. Signup and view all the answers

What refers to the truth or falsity of a statement?

Truth Value Signup and view all the answers

What is the opposite meaning and opposite truth value called?

Negation Signup and view all the answers

What is a compound statement?

Two or more statements joined by the word and. Signup and view all the answers

What is a conjunction?

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

What is a disjunction?

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

What is a convenient method for organizing the truth values of statements?

Truth Table Signup and view all the answers

What is it called when exchanging the hypothesis and conclusion of the conditional?

Converse Signup and view all the answers

What is the inverse of a conditional statement?

Negating both the hypothesis and conclusion of the conditional. Signup and view all the answers

What is the contrapositive of a conditional statement?

Negating both the hypothesis and conclusion of the converse statement. Signup and view all the answers

What is a biconditional statement?

The conjunction of a conditional and its converse. Signup and view all the answers

What is the Law of Detachment?

If p→q is true and p is true, then q is also true. Signup and view all the answers

What is the Law of Syllogism?

If p→q and q→r are true, then p→r is also true. Signup and view all the answers

Through any two points there is _____

exactly one line Signup and view all the answers

Through any three points not on the same line there is _____

exactly one plane Signup and view all the answers

A line contains at least _____

two points Signup and view all the answers

If two planes intersect, then _____

their intersection is a line Signup and view all the answers

Two lines intersect at _______

exactly one point Signup and view all the answers

What does the midpoint theorem state?

If M is the midpoint of AB, then AM≅MB. Signup and view all the answers

If two angles are vertical angles, what can be said about them?

They are congruent. Signup and view all the answers

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.

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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.

Glencoe Geometry Chapter 2 Quiz

Questions and Answers

What is an educated guess based on known information?

What is an example used to show that a given statement is not always true?

What type of statement can be written in if-then form?

What is the form if p, then q referred to as?

What is the phrase that follows the word if in a conditional statement?

What is the phrase that follows the word then in a conditional statement?

What reasoning uses facts, definitions, or properties to reach logical conclusions?

What is a statement that is accepted as true without proof called?

What is a paragraph written to explain why a conjecture for a given situation is true called?

What contains statements and reasons organized in two columns to prove conjectures and theorems?

What property is represented by ∠1≅∠1?

What theorem states that if ∠1≅∠2, then ∠2≅∠1?

What theorem asserts that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?

Examining several specific situations to arrive at a conjecture (prediction or plausible generalization) is called _____.

What is represented by (AB) ̅≅(AB) ̅?

What theorem states that if (AB) ̅≅(CD) ̅, then (CD) ̅≅(AB) ̅?

What theorem asserts that if (AB) ̅≅(CD) ̅ and (CD) ̅≅(EF), then (AB) ̅≅(EF) ̅?

What are the five parts of a good proof?

What theorem states that if ∠1≅∠2, then ∠2≅∠1?

What theorem states that if ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3?

If two angles form a linear pair, what can be said about them?

If the noncommon sides of two adjacent angles form a right angle, what can be said about them?

What is a statement?

What refers to the truth or falsity of a statement?

What is the opposite meaning and opposite truth value called?

What is a compound statement?

What is a conjunction?

What is a disjunction?

What is a convenient method for organizing the truth values of statements?

What is it called when exchanging the hypothesis and conclusion of the conditional?

What is the inverse of a conditional statement?

What is the contrapositive of a conditional statement?

What is a biconditional statement?

What is the Law of Detachment?

What is the Law of Syllogism?

Through any two points there is _____

Through any three points not on the same line there is _____

A line contains at least _____

If two planes intersect, then _____

Two lines intersect at _______

What does the midpoint theorem state?

If two angles are vertical angles, what can be said about them?

Study Notes

Key Definitions in Geometry

Components of Conditional Statements

Logical Reasoning

Types of Proof

Properties of Congruence

Additional Properties for Segments

Important Theorems

Statements and Truth Values

Compound Statements

Truth Tables

Conditional Logic Transformations

Laws of Logic

Geometric Principles

Midpoint and Congruency

Studying That Suits You

Description

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