Geometry Chapter 2 Flashcards
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Questions and Answers

What does 'conjecture' mean?

  • A theorem
  • A statement supported by proof
  • An unproven statement based on observation (correct)
  • A mathematical law

    • What does 'inductive' refer to?

    Finding the pattern

    What is a conditional statement?

    Hypothesis and conclusion, if then

    What is the meaning of 'negation'?

    <p>Opposite of conditional</p> Signup and view all the answers

    What is meant by 'converse'?

    <p>Swap places of Conditional</p> Signup and view all the answers

    What does 'inverse' refer to?

    <p>Negation of conditional</p> Signup and view all the answers

    What is 'contrapositive'?

    <p>Negation of converse</p> Signup and view all the answers

    What does 'deductive' mean?

    <p>Statement, facts</p> Signup and view all the answers

    What is the 'Law of Detachment'?

    <p>If the hypothesis is true, then the conclusion must be true as well</p> Signup and view all the answers

    What does the 'Law of Syllogism' state?

    <p>If p -&gt; q and q -&gt; r are true conditional statements, then p -&gt; r is true</p> Signup and view all the answers

    What is the 'Addition Property'?

    <p>If a = b, then a + c = b + c</p> Signup and view all the answers

    What does the 'Subtraction Property' state?

    <p>If a = b, then a - c = b - c</p> Signup and view all the answers

    What is the 'Multiplication Property'?

    <p>If a = b, then a * c = b * c</p> Signup and view all the answers

    What is the 'Division Property'?

    <p>If a = b, then a / c = b / c</p> Signup and view all the answers

    What does the 'Substitution Property' involve?

    <p>If a = b then a can be substituted for b and vice versa</p> Signup and view all the answers

    What is the 'Distributive Property'?

    <p>If a = b, then c(a + a) = ac + bc</p> Signup and view all the answers

    What does the 'Reflexive Property' state?

    <p>a = a</p> Signup and view all the answers

    What is the 'Symmetric Property'?

    <p>If a = b, then b = a</p> Signup and view all the answers

    What does the 'Transitive Property' state?

    <p>If a = b, and b = c, then a = c</p> Signup and view all the answers

    What is a 'theorem'?

    <p>A relationship useful for writing proofs</p> Signup and view all the answers

    What does the 'Right Angle Congruence Theorem' state?

    <p>All right angles are congruent</p> Signup and view all the answers

    What is the 'Congruent Supplement Theorem'?

    <p>If two angles are supplements of the same angle (or congruent angle), then two angles are congruent</p> Signup and view all the answers

    What does the 'Congruent Complement Theorem' state?

    <p>If two angles are complements of the same angle or congruent angle, then the two angles are congruent</p> Signup and view all the answers

    What is a 'postulate'?

    <p>Something we cannot prove but know that it is true</p> Signup and view all the answers

    What does the 'Vertical Angle Congruence Theorem' state?

    <p>Vertical angles are congruent</p> Signup and view all the answers

    What is the 'Quadratic Formula'?

    <p>x = -b ± √(b² - 4ac)/2a</p> Signup and view all the answers

    What is the 'Quadratic Maximum Formula'?

    <p>-b/2a</p> Signup and view all the answers

    What does the 'Property of Equality' indicate?

    <p>When an equal sign is used</p> Signup and view all the answers

    What is the 'Property of Congruency'?

    <p>When a congruency sign is used</p> Signup and view all the answers

    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.

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