Geometry 1A 2 Inverse and Contrapositive

Front

What is a conditional statement?

Back

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."

Front

What is the inverse of a conditional statement?

Back

The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion. For example, 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 a conditional statement is formed by negating both the hypothesis and conclusion and switching their places. For example, the contrapositive of "If P, then Q" is "If not Q, then not P."

Front

What is the relationship between a conditional statement and its contrapositive?

Back

A conditional statement and its contrapositive are logically equivalent, meaning they have the same truth value.

Front

What is the relationship between a conditional statement and its inverse?

Back

A conditional statement and its inverse are not logically equivalent; they can have different truth values.

Front

What is an example of a conditional statement?

Back

"If an angle is greater than 90 degrees, then it is obtuse."

Front

What is an example of an inverse statement?

Back

The inverse of "If an angle is greater than 90 degrees, then it is obtuse" is "If an angle is not greater than 90 degrees, then it is not obtuse."

Front

What is an example of a contrapositive statement?

Back

The contrapositive of "If an angle is greater than 90 degrees, then it is obtuse" is "If an angle is not obtuse, then it is not greater than 90 degrees."

Front

How do you form the inverse of the statement "If 2 lines are parallel, then they never touch"?

Back

The inverse is "If 2 lines are not parallel, then they touch."

Front

How do you form the contrapositive of the statement "If a number can be divided by 2, then it is even"?

Back

The contrapositive is "If a number is not even, then it cannot be divided by 2."