The conditional statement needs to be clarified before we can write the five conditionals.
See solution.
Practice makes perfect
We need to write the given statement as an if-then statement then write the converse, inverse, contrapositive, and bi-conditional statements. Let's start with the if-then statement.
If-Then
If-then statements take a specific form.
&If p,
&then q.
Here, p is the hypothesis and q is the conclusion. For this exercise, we are told that "Supplementary angles sum to 180^(∘)." Therefore, a logical if-them statement would be as follows.
&If two angles are supplementary,
&then the sum of their measures is 180^(∘).
Converse
When we write the converse, we swap the hypothesis and the conclusion.
&If the sum of the measures of two angles is 180^(∘),
&then the two angles are supplementary.
Inverse
When we write the inverse, we negate the hypothesis and conclusion in the original conditional statement.
&If two angles are not supplementary,
&then the sum of their measures is not 180^(∘).
Contrapositive
When we write the contrapositive, we negate the hypothesis and conclusion in the converse.
&If the sum of the measures of two angles is not 180^(∘),
&then the two angles are not supplementary.
Bi-Conditional
Bi-conditional statements use "if and only if" to show that a conditional statement works both ways. Since two lines will always form a point if they intersect, we can write the following bi-conditional statement.
&Two angles are supplementary,
&if and only if the sum of their measures is180^(∘).
