What is a converse of a theorem that is an if-then statement? (1 point) • The if part and the then part switch places. • The two parts are negated by using the word not. • The converse of a theorem has no relationship to the original theorem. • The converse is the same as the original theorem.
The converse of a theorem that is an if-then statement is:
- The if part and the then part switch places.
The converse of a theorem that is an if-then statement is when the if part and the then part switch places. Therefore, the correct answer is: • The if part and the then part switch places.
The converse of a theorem that is an if-then statement corresponds to the first option: "The if part and the then part switch places."
To understand the converse, it is important to know that an if-then statement has two parts: the hypothesis (the "if" part) and the conclusion (the "then" part). In the converse, the positions of these two parts are swapped. Essentially, the original statement is reversed.
For example, let's say we have the original if-then statement: "If it is raining, then the ground is wet." The hypothesis is "it is raining," and the conclusion is "the ground is wet."
The converse of this statement would be: "If the ground is wet, then it is raining." Here, the hypothesis and the conclusion have been switched.
It is important to note that the converse of a theorem may or may not be true. In some cases, the converse of a true theorem is also true, which can be used to prove other theorems. However, in other cases, the converse is false, indicating that the original statement is not necessarily true in the opposite direction.