Algebra Proofs and Concepts Flashcards
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Algebra Proofs and Concepts Flashcards

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Questions and Answers

What is a proof?

  • An opinion based discussion
  • A collection of examples
  • A logical argument that shows a statement is true (correct)
  • A set of equations
  • What is an algebraic proof?

    A proof that is made up of a series of algebraic statements.

    What is a two-column proof?

    A type of proof written as numbered statements and reasons that show the logical order of an argument.

    What are parallel lines?

    <p>Lines in the same plane that never intersect.</p> Signup and view all the answers

    What does the Addition Property of Equality state?

    <p>If you add the same number to each side of an equation, the two sides remain equal.</p> Signup and view all the answers

    What is the Multiplication Property of Equality?

    <p>If you multiply each side of an equation by the same nonzero number, the two sides remain equal.</p> Signup and view all the answers

    What are vertical angles?

    <p>A pair of opposite congruent angles formed by intersecting lines.</p> Signup and view all the answers

    What are supplementary angles?

    <p>Two angles whose sum is 180 degrees.</p> Signup and view all the answers

    What is a linear pair?

    <p>Two adjacent angles whose noncommon sides are opposite rays.</p> Signup and view all the answers

    What is an obtuse angle?

    <p>An angle that measures more than 90 degrees but less than 180 degrees.</p> Signup and view all the answers

    What is an acute angle?

    <p>An angle that measures less than 90 degrees.</p> Signup and view all the answers

    What is a right angle?

    <p>An angle that measures 90 degrees.</p> Signup and view all the answers

    What is an angle bisector?

    <p>A ray that divides an angle into two congruent angles.</p> Signup and view all the answers

    What is a perpendicular bisector?

    <p>A line that is perpendicular to a segment at its midpoint.</p> Signup and view all the answers

    What does the Subtraction Property of Equality state?

    <p>If you subtract the same number from each side of an equation, the two sides remain equal.</p> Signup and view all the answers

    Study Notes

    Proof Concepts

    • Proof: A logical argument demonstrating that a statement is true.
    • Algebraic Proof: Composed of a sequence of algebraic statements that validate a conclusion.
    • Two-Column Proof: Structured with numbered statements and corresponding reasons, illustrating the logical flow of the argument.

    Geometry Terms

    • Parallel Lines: Lines existing in the same plane that do not intersect at any point.
    • Vertical Angles: A pair of angles that are opposite each other when two lines intersect; they are always congruent.
    • Supplementary Angles: Two angles where the sum of their measures is 180 degrees.
    • Linear Pair: Two adjacent angles that share a common side and whose noncommon sides form opposite rays.

    Angle Types

    • Obtuse Angle: An angle measuring between 90 degrees and 180 degrees.
    • Acute Angle: An angle measuring less than 90 degrees.
    • Right Angle: An angle that measures exactly 90 degrees.

    Angle Properties

    • Angle Bisector: A ray that splits an angle into two equal (congruent) angles.
    • Perpendicular Bisector: A line that intersects a segment at its midpoint, forming right angles with that segment.

    Properties of Equality

    • Addition Property of Equality: States that adding the same value to both sides of an equation keeps the equation balanced.
    • Subtraction Property of Equality: Indicates that subtracting the same value from both sides of an equation maintains its equality.
    • Multiplication Property of Equality: Asserts that multiplying both sides of an equation by the same nonzero number preserves the equation's balance.

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    Description

    This quiz provides essential definitions related to algebra proofs, including terms such as logical arguments, algebraic proofs, and two-column proofs. It's an excellent resource for understanding the structure and reasoning involved in proving mathematical statements using algebra.

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