Reasoning and Proof review CH. 2

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What is a counterexample?

Back

A counterexample is an example that disproves a statement or proposition. For instance, the statement 'Every prime number is an odd number' is disproved by the counterexample '2', which is a prime number but not odd.

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What is the converse of a conditional statement?

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The converse of a conditional statement 'If P, then Q' is 'If Q, then P'. For example, the converse of 'If it is night, then it is dark outside' is 'If it is dark outside, then it is night'.

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What is the Supplements Theorem?

Back

The Supplements Theorem states that if two angles are supplementary to the same angle (or to congruent angles), then they are congruent to each other.

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What is a biconditional statement?

Back

A biconditional statement is a statement that combines a conditional statement and its converse, written as 'P if and only if Q'. It is true when both the original statement and the converse are true.

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What does it mean for angles to be supplementary?

Back

Two angles are supplementary if the sum of their measures is 180 degrees.

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What is a conditional statement?

Back

A conditional statement is an 'if-then' statement that expresses a relationship between two propositions, typically written as 'If P, then Q'.

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'. It is logically equivalent to the original statement.

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What is the difference between a theorem and a postulate?

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A theorem is a statement that has been proven based on previously established statements, such as other theorems, while a postulate is a statement accepted as true without proof.

Front

What is the definition of congruent angles?

Back

Congruent angles are angles that have the same measure.

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What is the Complement Theorem?

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The Complement Theorem states that if two angles are complementary to the same angle (or to congruent angles), then they are congruent to each other.