Question

instructions: answer the following questions in your notebook. 1. write the conditional for each statement: a. a number is even if it is divisible by 2. b. an angle is right when it measures 90°. 2. write the converse of each conditional. a. if a number is divisible by 2, then it is even. b. if an angle measures 90°, then it is a right angle 3. decide: o is the conditional true? o is the converse true? 4. think: o when both the conditional and converse are true, what does that tell us about the relationship between the two statements?

Explanation:

Step1: Write the conditional statements

a. The conditional statement for "A number is even if it is divisible by 2" is "If a number is divisible by 2, then it is even".
b. The conditional statement for "An angle is right when it measures 90°" is "If an angle measures 90°, then it is a right - angle".

Step2: Write the converse statements

a. The converse of "If a number is divisible by 2, then it is even" is "If a number is even, then it is divisible by 2".
b. The converse of "If an angle measures 90°, then it is a right - angle" is "If an angle is a right - angle, then it measures 90°".

Step3: Determine truth values

a. The conditional "If a number is divisible by 2, then it is even" is true. The converse "If a number is even, then it is divisible by 2" is also true.
b. The conditional "If an angle measures 90°, then it is a right - angle" is true. The converse "If an angle is a right - angle, then it measures 90°" is also true.

Step4: Analyze the relationship

When both the conditional and the converse are true, the two statements are logically equivalent.

Answer:

1.
a. If a number is divisible by 2, then it is even.
b. If an angle measures 90°, then it is a right - angle.
2.
a. If a number is even, then it is divisible by 2.
b. If an angle is a right - angle, then it measures 90°.
3.
a. The conditional is true. The converse is true.
b. The conditional is true. The converse is true.

1. The two statements are logically equivalent.