Geometry - Logic and Reasoning Review

Front

What type of statement is defined as true in both directions, such as 'an angle is a right angle if and only if its measure is 90°'?

Back

Biconditional

Front

What is a counterexample in logic?

Back

An example that disproves a statement or conjecture.

Front

Provide a counterexample for the statement: 'If a polygon is a quadrilateral, then it is a trapezoid.'

Back

A rectangle is a counterexample because it is a quadrilateral that is not a trapezoid.

Front

What is the term for reasoning that uses facts, definitions, accepted properties, and the laws of logic?

Back

Deductive reasoning.

Front

What is the Law of Syllogism in logic?

Back

If 'If A, then B' and 'If B, then C' are true, then 'If A, then C' is also true.

Front

What is the difference between inductive and deductive reasoning?

Back

Inductive reasoning involves making generalizations based on specific observations, while deductive reasoning involves applying general principles to reach specific conclusions.

Front

What is a conditional statement?

Back

A statement that can be written in the form 'If P, then Q'.

Front

What is the converse of a conditional statement?

Back

The converse of 'If P, then Q' is 'If Q, then P'.

Front

What is the inverse of a conditional statement?

Back

The inverse of 'If P, then Q' is 'If not P, then not Q'.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of 'If P, then Q' is 'If not Q, then not P'.