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 "Right angles are 90^(∘)." Therefore, a logical if-them statement would be as follows.
&If an angle is a right angle,
&then its measure is90^(∘).
Converse
When we write the converse, we swap the hypothesis and the conclusion.
&If an angle measures90^(∘),
&then it is a right angle.
Inverse
When we write the inverse, we negate the hypothesis and conclusion in the original conditional statement.
&If an angle is not a right angle,
&then its measure is not90^(∘).
Contrapositive
When we write the contrapositive, we negate the hypothesis and conclusion in the converse.
&If an angle's measure is not90^(∘),
&then it is not a right angle.
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.
&An angle is a right angle,
&if and only if its measure is90^(∘).
