Answer :
Answer:
The four true statements are:
1. If an angle is a right angle, it measures 90°.
2. If an angle measures 90°, it is a right angle.
3. If an angle is not a right angle, it does not measure measure 90°.
4. If an angle does not measure 90°, it is not a right angle.
Step-by-step explanation:
Given the biconditional statement:
An angle is a right angle if and only if it measures 90°.
To find:
Four true conditional statements.
Solution:
First of all, let us the learn the concept of four true conditional statements from a given biconditional statement.
Let the biconditional statement be "[tex]a[/tex] is true if and only if [tex]b[/tex] is true.
Then the four true statements can be written as:
1. If [tex]a[/tex] is true then [tex]b[/tex] is true.
2. If [tex]b[/tex] is true then [tex]a[/tex] is true.
3. If [tex]a[/tex] is false then [tex]b[/tex] is false.
4. If [tex]b[/tex] is false then [tex]a[/tex] is false.
Here [tex]a[/tex] is "an angle is a right angle"
[tex]b[/tex] is "it measures 90°" .
So, the four true statements are:
1. If an angle is a right angle, it measures 90°.
2. If an angle measures 90°, it is a right angle.
3. If an angle is not a right angle, it does not measure measure 90°.
4. If an angle does not measure 90°, it is not a right angle.