Podcast
Questions and Answers
What is a proof?
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?
What is an algebraic proof?
A proof that is made up of a series of algebraic statements.
What is a two-column proof?
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?
What are parallel lines?
What does the Addition Property of Equality state?
What does the Addition Property of Equality state?
What is the Multiplication Property of Equality?
What is the Multiplication Property of Equality?
What are vertical angles?
What are vertical angles?
What are supplementary angles?
What are supplementary angles?
What is a linear pair?
What is a linear pair?
What is an obtuse angle?
What is an obtuse angle?
What is an acute angle?
What is an acute angle?
What is a right angle?
What is a right angle?
What is an angle bisector?
What is an angle bisector?
What is a perpendicular bisector?
What is a perpendicular bisector?
What does the Subtraction Property of Equality state?
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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