Algebraic Proofs Examples Flashcards
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Questions and Answers

What does 'Given' refer to in the context of algebraic proofs?

  • 11x-8 = 9x+4
  • ∠ W ≅ ∠ Z (correct)
  • m∠ w = m∠c
  • 2x-8 = 4
  • What does 'Definition of congruency' refer to in algebraic proofs?

  • m∠ w = m∠c (correct)
  • FG ≅ JH
  • X = 6
  • 2x = 12
  • What does 'Substitution property of equality' imply in algebraic proofs?

  • ∠ ABD ≅ ∠ EBC
  • X = 6
  • 2x = 12
  • 11x-8 = 9x+4 (correct)
  • What does 'Subtraction property of equality' state?

    <p>2x - 8 = 4</p> Signup and view all the answers

    What does 'Addition property of equality' refer to?

    <p>2x = 12</p> Signup and view all the answers

    What does 'Division property of equality' state?

    <p>X = 6</p> Signup and view all the answers

    What is implied by the 'Transitive property'?

    <p>∠ ABD ≅ ∠ EBC</p> Signup and view all the answers

    What does the 'Transitive property' suggest in congruency?

    <p>FG ≅ JH</p> Signup and view all the answers

    What does the 'Definition of congruency' state in algebraic terms?

    <p>FG = JH</p> Signup and view all the answers

    What does the 'Symmetric property' indicate?

    <p>4 = x to x = 4</p> Signup and view all the answers

    Study Notes

    Algebraic Proofs Fundamentals

    • Given indicates the established facts, such as angles that are congruent, e.g., ∠ W ≅ ∠ Z.

    Definition of Congruency

    • Congruency definition involves the equality of angle measures, exemplified by m∠w = m∠c.

    Substitution Property of Equality

    • This property allows for the replacement of one expression with another equal expression, illustrated by the equation 11x - 8 = 9x + 4.

    Subtraction Property of Equality

    • This property states that if two expressions are equal, subtracting the same value from both sides maintains equality, demonstrated by 2x - 8 = 4.

    Addition Property of Equality

    • When both sides of an equation are increased by the same amount, equality is preserved, seen in the equation 2x = 12.

    Division Property of Equality

    • This principle allows dividing both sides of an equation by the same non-zero number, illustrated by the solution x = 6.

    Transitive Property

    • If two quantities are each equal to a third quantity, they are equal to each other, as seen with ∠ ABD ≅ ∠ EBC.

    Transitive Property in Congruency

    • Similar to equality, congruent segments or angles can be linked; for instance, if FG ≅ JH, then FG and JH are congruent.

    Definition of Congruency in Measurements

    • The measure of congruent segments or angles are equal, e.g., FG = JH signifies the equality of length or angle measure.

    Symmetric Property

    • This property states that if one quantity equals another, the second quantity equals the first; showcased by the transition from 4 = x to x = 4.

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    Test your understanding of algebraic proofs with this flashcard quiz. Each card presents a key concept or property related to congruency and equality used in algebraic proofs. Review definitions and identify the steps to strengthen your knowledge in algebra.

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