Algebra Proofs and Concepts Flashcards

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.

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.