Unit 3 Review (Logical Reasoning)

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What is a conditional statement?

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A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). For example, "If it rains, then the ground is wet."

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What is the converse of a conditional statement?

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The converse of a conditional statement is formed by reversing the hypothesis and conclusion. For example, the converse of "If it rains, then the ground is wet" is "If the ground is wet, then it rains."

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What is the inverse of a conditional statement?

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The inverse of a conditional statement is formed by negating both the hypothesis and conclusion. For example, the inverse of "If it rains, then the ground is wet" is "If it does not rain, then the ground is not wet."

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion and then reversing them. For example, the contrapositive of "If it rains, then the ground is wet" is "If the ground is not wet, then it does not rain."

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What is a counterexample?

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A counterexample is an example that disproves a statement or proposition. For instance, the statement "If a number is divisible by 3, then it is odd" can be disproven by the counterexample of 6, which is even but divisible by 3.

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What does it mean for a converse to be true?

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A converse is true if the conclusion of the original conditional statement is true whenever the hypothesis is true. For example, the converse of "If a figure is a trapezoid, then it is a quadrilateral" is true.

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What is a biconditional statement?

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A biconditional statement is a statement that combines a conditional statement and its converse, typically expressed as "p if and only if q". It is true when both p and q are either true or false.

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What is the definition of congruent angles?

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Congruent angles are angles that have the same measure. If two angles are congruent, their measures are equal.

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What is the definition of supplementary angles?

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Supplementary angles are two angles whose measures add up to 180 degrees.

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What is the definition of a linear pair?

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A linear pair is a pair of adjacent angles formed when two lines intersect. The angles in a linear pair are supplementary.