Mr. Garret wrote the statement below on the chalkboard.

"If two rays have the same endpoint, then they are opposite rays."

Which of the following is the converse of the statement below?

A. Opposite rays have the same endpoint.
Incorrect. This is not the converse of the original statement.

B. If two rays have the same endpoint, then they are opposite rays.
Incorrect. This is the conditional statement, find the converse.

C. If two rays are opposite rays, they have the same endpoint.
Correct! This is the converse of the original statement.

D. An angle is formed when two rays have the same endpoint.
Incorrect. This is not the converse of the original statement.

Determine the inverse of the following conditional statement.

If the m∠C = 122°, then ∠C is an obtuse angle.

1. If the m∠C = 122°, then ∠C is an obtuse angle.
   Incorrect. This is the conditional statement.
2. If the angle is an obtuse angle, then it measures 122°.
   Incorrect. This is the converse statement.
3. If the angle is not an obtuse angle, then it does not measure 122°.
   Incorrect. This is the contrapositive statement.
4. If the m∠C ≠ 122°, then ∠C is not an obtuse angle.
   Correct! The inverse statement should be in the form “if not p then not q”.

The contrapositive of a statement is given below.

If an angle is not an acute angle, then it does not measure less then 90°.

What is the conditional statement?

1. If an angle measures less than 90°, then it is an acute angle.
   Correct! This is the conditional statement.
2. If an angle is an acute angle, then it measures less then 90°.
   Incorrect. This is the converse statement.
3. If an angle does not measure 90°, then it is not an acute angle.
   Incorrect. This is the inverse statement.
4. If an angle is not an acute angle, then it does not measure less then 90°.
   Incorrect. This is the given contrapositive statement.

The inverse of a statement is given below.

If I am not busy, then I am not doing homework.

What is the converse of this statement?

A. If I am busy, then I am doing homework.
Incorrect. This is the conditional statement.

B. If I am doing homework, then I am busy.
Correct! This is the converse statement.

C. If I am not doing homework, then I am not busy.
Incorrect. This is the contrapositive statement.

D. If I am not busy, then I'm not doing homework.
Incorrect. This is the inverse statement.