2.3 Biconditionals

2.3 Biconditionals

Geometry CP

Biconditional Review

• A statement that contains the phrase "if and only if."

• "if and only if" is abbreviated using iff

To determine if a statement is a true biconditional, both the conditional and converse must be true!

• Conditional: If the shape has 3 sides, then it is a triangle.

• Converse: If it is a triangle, then the shape has 3 sides.

• Conditional is TRUE, Converse is TRUE, so Biconditional is TRUE.

To determine if a statement is a true biconditional, both the conditional and converse must be true!

• Conditional: If it is a square, then the shape has 4 sides.

• Converse: If the shape has 4 sides, then it is a square.

• Conditional is TRUE, Converse is FALSE, so Biconditional is FALSE.

Multiple Choice

What is the conditional statement from the following biconditional:

Two angles are supplementary if and only if the sum of their measures is 180°.

• If the sum of their measures is 180º, then two angles are supplementary.

• If two angles are supplementary, then the sum of their measures is 180º.

Multiple Choice

What is the converse statement from the following biconditional:

Two angles are supplementary if and only if the sum of their measures is 180°.

• If the sum of their measures is 180º, then two angles are supplementary.

• If two angles are supplementary, then the sum of their measures is 180º.

Multiple Choice

What is the conditional statement from the following biconditional:

Three points are collinear iff all three points lie on the same line.

• If three points are collinear, then all three points lie on the same line.

• If all three points lie on the same line, then three points are collinear.

Multiple Choice

What is the converse statement from the following biconditional:

Three points are collinear iff all three points lie on the same line.

• If three points are collinear, then all three points lie on the same line.

• If all three points lie on the same line, then three points are collinear.

Fill in the Blank

Write the conditional of the following biconditional statement:

An animal is a dog iff it has fur.

Fill in the Blank

Write the converse of the following biconditional statement:

An animal is a dog iff it has fur.

How to write a conditional as a biconditional

• If two segments are the same size, then they are congruent.

• Cross out the IF and the THEN.

• Rewrite the statement using IFF in the spot where the "then" used to be.

• Two segments are the same size iff they are congruent.

Fill in the Blank

Write the biconditional of:

If today is Friday, then tomorrow is Saturday.

Fill in the Blank

Write the biconditional of:

If this month is September, then last month was August.

TRUE vs. FALSE Biconditionals

• If ...

• the conditional statement is true

• the converse statement is true

• then the biconditional is true.

Multiple Choice

Is the biconditional true or false?

Biconditional: It is Saturday iff I do not have school.

Conditional: If it is Saturday, then I do not have school.

Converse: If I do not have school, then it is Saturday.

• True

• False

Multiple Choice

Is the biconditional true or false?

Biconditional: Three points are coplanar if and only if they lie in the same plane.

Conditional: If three points are coplanar, then they lie in the same plane.

Converse: If they lie in the same plane, the three points are coplanar.

• True

• False