Questions and Answers
What is the definition of a Conditional Statement?
What is the converse of a conditional statement?
If q, then p
What does the inverse of a conditional statement state?
If not p, then not q
What is the contrapositive of a conditional statement?
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Through any two points there exists exactly one line.
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A line contains at least two points.
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If two lines intersect, then their intersection is a line.
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Through any three noncollinear points, there exists exactly one plane.
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If two points lie in a plane, then the line containing them lies in the plane.
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What is inductive reasoning?
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What is deductive reasoning?
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The Law of Detachment states that if the hypothesis of a true conditional statement is true, then the conclusion is also false.
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What does the Law of Syllogism state?
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What is the negation of a statement?
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What is a biconditional statement?
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What are equivalent statements?
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Two lines that intersect form a right angle.
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What defines proof in geometry?
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If two angles form a linear pair, then they are supplementary.
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What does the Reflexive Property of Segment Congruence state?
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What does the Symmetric Property of Segment Congruence state?
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What does the Transitive Property of Segment Congruence state?
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What does the Reflexive Property of Angle Congruence state?
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What does the Symmetric Property of Angle Congruence state?
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What does the Transitive Property of Angle Congruence state?
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All right angles are congruent.
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If two angles are supplementary to the same angle, then they are congruent.
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If a = b, then a + c = b + c.
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If a = b, then a - c = b - c.
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If a = b, then ac = bc, c ≠ 0.
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If a = b, then a/c = b/c, c ≠ 0.
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If a = b, then a can always be substituted for b.
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What does the Distributive Property state?
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The Reflexive Property states that a = a.
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The Symmetric Property states that if a = b, then b = a.
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The Transitive Property states that if a = b and b = c, then a = c.
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Study Notes
Conditional Statements and Reasoning
- Conditional Statement: An "if-then" logical statement with a hypothesis and conclusion.
- Converse: Created by switching the hypothesis and conclusion of a conditional statement.
- Inverse: Negates both the hypothesis and conclusion of a conditional statement.
- Contrapositive: The inverse of the converse; negates the conclusion and hypothesis.
- Inductive Reasoning: Involves finding patterns to make conjectures.
- Deductive Reasoning: Uses established facts and logical laws to form arguments.
- Law of Detachment: If a true conditional statement's hypothesis is true, then its conclusion must also be true.
- Law of Syllogism: Connects two true statements: if p → q and q → r, then p → r is true.
Properties of Logic and Statements
- Negation: Denoted as "~p", it represents the opposite of the original statement.
- Biconditional Statement: "If and only if", indicating a two-way logical relationship.
- Equivalent Statements: Related conditional statements that share the same truth value, both true or both false.
Geometric Postulates
- Two Point Postulate: Guarantees that through any two points, there exists exactly one line.
- Line-Point Postulate: States that a line must contain a minimum of two points.
- Line Intersection Postulate: If two lines intersect, their intersection is one unique point.
- Three Point Postulate: Asserts that through any three noncollinear points, exactly one plane exists.
- Plane Point Postulate: Indicates a plane must contain at least three noncollinear points.
- Plane-Line Postulate: If two points lie in a plane, the line connecting them lies in the same plane.
- Plane Intersection Postulate: The intersection of two planes is a line.
Angle and Segment Congruence Theorems
- Perpendicular Lines: Defined as two lines intersecting at a right angle.
- Linear Pair Postulate: States that two angles forming a linear pair are supplementary.
- Reflexive Property of Segment Congruence: Any segment equals itself (AB ≅ AB).
- Symmetric and Transitive Properties of Segment Congruence: If AB ≅ CD, then CD ≅ AB; if AB ≅ CD and CD ≅ EF, then AB ≅ EF.
- Reflexive, Symmetric, and Transitive Properties of Angle Congruence: Each angle equals itself and follows similar properties as segments.
- Right Angles Congruence Theorem: All right angles are congruent.
- Congruent Supplement and Complement Theorems: If two angles supplement or complement the same angle, they are congruent.
- Vertical Angles Congruence Theorem: Vertical angles are congruent.
Properties of Equality
- Addition, Subtraction, Multiplication, and Division Properties of Equality: Fundamental rules for manipulating equalities involving the same operations on both sides.
- Substitution Property of Equality: If a equals b, a can be substituted for b in any mathematical expression.
- Distributive Property: Applied to sums and differences, allowing distribution of multiplication over addition or subtraction.
- Reflexive, Symmetric, and Transitive Properties of Equality: Reflects that equal quantities are the same, interchangeable, and linked through transitive relations.
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Prepare for your Geometry Chapter 2 test with these flashcards. Learn key terms such as conditional statements, converses, and inverses, which are essential for understanding logical reasoning in geometric concepts. Master these definitions to succeed in your exam.
