Questions and Answers
What does 'conjecture' mean?
What does 'inductive' refer to?
Finding the pattern
What is a conditional statement?
Hypothesis and conclusion, if then
What is the meaning of 'negation'?
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What is meant by 'converse'?
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What does 'inverse' refer to?
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What is 'contrapositive'?
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What does 'deductive' mean?
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What is the 'Law of Detachment'?
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What does the 'Law of Syllogism' state?
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What is the 'Addition Property'?
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What does the 'Subtraction Property' state?
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What is the 'Multiplication Property'?
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What is the 'Division Property'?
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What does the 'Substitution Property' involve?
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What is the 'Distributive Property'?
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What does the 'Reflexive Property' state?
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What is the 'Symmetric Property'?
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What does the 'Transitive Property' state?
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What is a 'theorem'?
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What does the 'Right Angle Congruence Theorem' state?
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What is the 'Congruent Supplement Theorem'?
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What does the 'Congruent Complement Theorem' state?
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What is a 'postulate'?
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What does the 'Vertical Angle Congruence Theorem' state?
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What is the 'Quadratic Formula'?
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What is the 'Quadratic Maximum Formula'?
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What does the 'Property of Equality' indicate?
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What is the 'Property of Congruency'?
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Study Notes
Geometry Terms and Definitions
- Conjecture: An unproven statement derived from observations; used as a basis for further investigation.
- Inductive Reasoning: The process of identifying patterns and deriving conclusions from specific examples.
- Conditional Statement: A logical statement that has a hypothesis and conclusion, typically structured in an "if-then" format.
- Negation: The inverse of a conditional statement, changing the truth value to its opposite.
- Converse: A statement formed by swapping the hypothesis and conclusion of a conditional statement.
- Inverse: The negation of the original conditional statement, reversing both the hypothesis and conclusion.
- Contrapositive: The negation of the converse; it involves reversing and negating both parts of the original conditional.
- Deductive Reasoning: Deriving specific conclusions from general principles or accepted facts.
Laws and Properties
- Law of Detachment: If the hypothesis of a conditional statement is true, then the conclusion must also be true.
- Law of Syllogism: If two conditional statements are true, and the conclusion of one statement serves as the hypothesis of the other, a new conditional statement can be inferred.
- Addition Property: If two quantities are equal, adding the same value to both maintains equality.
- Subtraction Property: If two quantities are equal, subtracting the same value from both retains equality.
- Multiplication Property: If two quantities are equal, multiplying both by the same number keeps them equal.
- Division Property: If two quantities are equal, dividing both by the same non-zero number preserves equality.
- Substitution Property: If two quantities are equal, one can be substituted for the other in expressions or equations.
- Distributive Property: Multiplication distributed over addition, where a(b + c) = ab + ac.
Properties of Equality and Congruency
- Reflexive Property: Any quantity is equal to itself (e.g., a = a).
- Symmetric Property: If one quantity equals another, then the second equals the first (if a = b, then b = a).
- Transitive Property: If one quantity equals a second, and the second equals a third, the first equals the third (if a = b and b = c, then a = c).
Theorems and Important Formulas
- Theorem: A proven statement or relationship that is used for constructing mathematical proofs.
- Right Angle Congruence Theorem: All right angles are congruent to each other.
- Congruent Supplement Theorem: Angles that are supplements of the same angle (or of congruent angles) are congruent.
- Congruent Complement Theorem: Angles that are complements of the same angle (or of congruent angles) are congruent.
- Vertical Angle Congruence Theorem: Vertical angles are always congruent.
- Postulate: A basic assumption accepted without proof; considered universally true.
Quadratic Equations
- Quadratic Formula: Used to find the roots of quadratic equations, given as x = [-b ± √(b² - 4ac)] / 2a.
- Quadratic Maximum Formula: Provides the x-coordinate of the vertex for a quadratic function, calculated as -b / 2a.
Properties and Signs
- Property of Equality: Fundamental principle stating that if two values are equal, they can be interchanged in equations.
- Property of Congruency: Similar to the property of equality but in terms of geometric figures and their congruence.
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Test your knowledge with these interactive flashcards covering key concepts from Chapter 2 of Geometry. Each card features important definitions and terms such as conjecture, inductive reasoning, and conditional statements. Ideal for quick reviews and enhancing your understanding of geometric principles.
