Section 2-2:Biconditionals and Definitions

Conditional:If two angles have the same measure, then

the angles are congruent.

Converse: If two angles are congruent, then the angles

have the same measure.

How can we combine both true statements?

We can combine a true conditional and true converse into a biconditional.

We do so by using the phrase “if and only if” to connect the hypothesis and conclusion.

Conditional:If two angles have the same measure, then

the angles are congruent.

Biconditional:Two angles have the same measure if and

only if the angles are congruent.

Remember, it is important for both the conditional AND its converse to be true in order to write a biconditional.

Conditional:If a figure is square, then it has four right angles.

Can this conditional be written as a biconditional?

No, because the converse is false.

Example: Write the biconditional for the following statement.

Conditional: If three points are collinear, then they lie on the

same line.

Three points are collinear if and only if they lie on the same line.

Homework:p. 90

#’s 1-17