Geometry Review: Proofs and Logic

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What is a conditional statement?

Back

A statement that can be written in the form 'if p, then q'.

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What is the inverse of a conditional statement?

Back

The statement formed by negating both the hypothesis and conclusion of the original conditional. If the original is 'if p, then q', the inverse is 'if not p, then not q'.

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What is the converse of a conditional statement?

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The statement formed by swapping the hypothesis and conclusion of the original conditional. If the original is 'if p, then q', the converse is 'if q, then p'.

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What is the contrapositive of a conditional statement?

Back

The statement formed by negating both the hypothesis and conclusion of the converse of the original conditional. If the original is 'if p, then q', the contrapositive is 'if not q, then not p'.

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What is inductive reasoning?

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A type of reasoning that involves making generalizations based on specific observations or patterns.

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What is the Law of Detachment?

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A law of logic stating that if a conditional statement 'if p, then q' is true, and p is true, then q must also be true.

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What is the Law of Syllogism?

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A law of logic stating that if 'if p, then q' and 'if q, then r' are true statements, then 'if p, then r' is also true.

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What are properties of equality?

Back

Rules that allow you to balance, manipulate, and solve equations, such as the reflexive, symmetric, and transitive properties.

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What are properties of congruence?

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Rules that apply to geometric figures, stating that figures are congruent if they have the same shape and size, including reflexive, symmetric, and transitive properties.

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What are angle theorems?

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Theorems related to angles, such as the Angle Addition Postulate, Vertical Angles Theorem, and Corresponding Angles Postulate.