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Questions and Answers
What is a proof?
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?
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What does the Addition Property of Equality state?
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What is the Multiplication Property of Equality?
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What are vertical angles?
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What are supplementary angles?
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What is a linear pair?
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What is an obtuse angle?
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What is an acute angle?
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What is a right angle?
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What is an angle bisector?
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What is a perpendicular bisector?
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What does the Subtraction Property of Equality state?
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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.