What is a converse of a theorem that is an if-then statement?
1. The two parts are negated by using the word not
2. The converse of a theorem has no relationship to the original theorem
3. The if part and the then part switch places
4. The converse is the same as the original theorem
3. The if part and the then part switch places
The converse of a theorem that is an if-then statement is obtained by switching the positions of the hypothesis (if part) and the conclusion (then part) of the original theorem. The converse statement is formed by reversing the direction of the implication.
To determine the converse of a theorem, you need to:
1. Identify the given if-then statement. For example, if the given theorem is "If it is raining, then the ground is wet."
2. Switch the positions of the hypothesis and conclusion. The converse statement would be "If the ground is wet, then it is raining."
3. Note that the converse statement may or may not be true. In many cases, the converse is not equivalent to the original theorem and could lead to a different conclusion. However, there are cases where the converse is true or equivalent to the original theorem.
So, the correct answer to your question is option 3: The if part and the then part switch places.