Glencoe Geometry Chapter 2 Quiz

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.