Untitled Quiz

Vocabulary Terms

• Conjecture: An unproven statement derived from observations.
• Counterexample: A particular case that disproves a conjecture.
• Conditional Statement: A logical structure combining a hypothesis and a conclusion.
• If-then Form: The format in which the hypothesis is introduced with "if" and the conclusion follows with "then".
• Negation: The statement that expresses the opposite of the original statement.
• Converse: A statement formed by reversing the hypothesis and conclusion of a conditional statement.
• Inverse: A statement formed by negating both the hypothesis and conclusion of a conditional statement.
• Contrapositive: Created by writing the converse of a conditional statement and negating both parts.
• Equivalent Statements: Statements that hold the same truth value, both true or both false.
• Biconditional Statement: A logical statement connecting two conditions with "if and only if".

Reasoning and Proof

• Deductive Reasoning: Involves reasoning from established facts and logical rules to arrive at conclusions.
• Law of Detachment: If the hypothesis of a true conditional statement is true, then the conclusion must also be true.
• Law of Syllogism: Allows one to conclude a direct connection between two conditional statements, forming a new conditional statement.

Geometry Concepts

• Line Perpendicular to a Plane: Exists if a line intersects a plane at a single point and is perpendicular to all lines through that point that lie in the plane.
• Proof: A structured logical argument demonstrating the truth of a statement.
• Two-column Proof: A method of proof that lists statements and their corresponding reasons side by side for clarity.

Theorems and Postulates

• Theorem: A statement that has been proven based on previously established statements and principles.
• Linear Pair Postulate: States that when two angles form a linear pair, they are supplementary.
• Vertical Angles Congruence Theorem: Claims that vertical angles are congruent.
• Congruent Complements Theorem: If two angles are each complementary to the same angle, they are congruent.
• Congruent Supplements Theorem: If two angles are supplementary to the same angle, they are congruent.
• Right Angles Congruence Theorem: Asserts that all right angles are congruent.
• Congruence of Angles Theorem: Describes the properties of angle congruence (reflexive, symmetric, transitive).
• Congruence of Segments Theorem: Outlines the properties of segment congruence (reflexive, symmetric, transitive).

Properties of Equality

• Reflexive Property: Every quantity is equal to itself (A=A).
• Symmetric Property: If one quantity equals a second, then the second quantity equals the first (If A=B, then B=A).
• Transitive Property: If one quantity equals a second, and that second quantity equals a third, then the first quantity equals the third (If A=B and B=C, then A=C).
• Distributive Property: Describes how to multiply a number by a sum (A(b+c)= ab+ac).
• Addition Property: States that if two quantities are equal, adding the same amount maintains the equality.
• Subtraction Property: States that subtracting the same amount from equal quantities keeps them equal.
• Multiplication Property: States that multiplying equal quantities by the same number keeps them equal.
• Division Property: States that dividing equal quantities by the same non-zero number keeps them equal.
• Substitution Property: Allows one to replace a quantity with equal quantity in any expression.

Important Skills

• Distinguish between inductive reasoning (used to form conjectures) and deductive reasoning (used to validate conjectures).
• Understand assumptions in mathematical statements and the limitations on what can be assumed.
• Skillfully articulate and construct proofs.
• Apply postulates and utilize diagrams effectively in problem-solving.
• Utilize algebraic properties for reasoning.
• Prove relationships concerning segments and angles, especially angle pair relationships.