Objective
To write biconditionals and recognize good definitions
In the Solve It, you used conditional statements. A biconditional is a single true statement that combines a true conditional and its true converse. You can write a biconditional by joining the two parts of each conditional with the phrase if and only if.
Essential Understanding A definition is good if it can be written as a biconditional.
What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional.
If the sum of the measures of two angles is 180, then the two angles are supplementary.
Converse: If two angles are supplementary, then the sum of the measures of the two angles is 180.
The converse is true. You can form a true biconditional by joining the true conditional and the true converse with the phrase if and only if.
How else can you write the biconditional?
You can also write the biconditional as “The sum of the measures of two angles is 180 if and only if the two angles are supplementary.”
Biconditional: Two angles are supplementary if and only if the sum of the measures of the two angles is 180.
What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional.
If two angles have equal measure, then the angles are congruent.