3-2 Biconditional Statements

Front

What is a biconditional statement?

Back

A biconditional statement is a statement that combines a conditional statement and its converse, expressed in the form 'P if and only if Q', meaning both P and Q are true or both are false.

Front

In order for a statement to be biconditional, both the conditional and converse statements need to be ____.

Back

true.

Front

What is the biconditional statement for 'If two lines have the same slope, then they are parallel' and 'If two lines are parallel, then they have the same slope'?

Back

Two lines are parallel if and only if they have the same slope.

Front

What is the biconditional statement for 'If two lines meet at 90 degrees, then they are perpendicular' and 'If two lines are perpendicular, then they meet at 90 degrees'?

Back

Two lines are perpendicular if and only if they meet at 90 degrees.

Front

Which of the following is a biconditional statement? 'If you do not vote, then you are not at least 18 years old.' or 'You can vote if and only if you are 18 years old.'

Back

You can vote if and only if you are 18 years old.

Front

What is the biconditional that matches the statement: 'A right angle is an angle with 90 degrees.'?

Back

An angle is a right angle if and only if it has 90 degrees.

Front

What does 'if and only if' signify in a biconditional statement?

Back

It signifies that both conditions must be true together or false together.

Front

Provide an example of a biconditional statement in geometry.

Back

A triangle is equilateral if and only if all its sides are equal.

Front

What is the converse of a conditional statement?

Back

The converse of a conditional statement 'If P, then Q' is 'If Q, then P'.

Front

How do you determine if a biconditional statement is true?

Back

A biconditional statement is true if both the original conditional and its converse are true.