AI Tutor
If it is pouring rain outside, the sidewalk is definitely wet. But if you see a wet sidewalk, does that mean it must be raining?
Of course not — someone could have just turned on a garden sprinkler! Flipping the order of cause and effect completely changes the meaning.
What happens when we apply this same flipping rule to geometric statements and proofs?

What Is a Converse?

A standard conditional statement has two parts: an if-clause called the hypothesis (pp) and a then-clause called the conclusion (qq), written symbolically as p→qp \rightarrow q.
The converse of a conditional statement is formed by simply switching the hypothesis and the conclusion: q→pq \rightarrow p.
If a conditional statement in geometry is true, does its converse have to be true as well?

Truth Value and Counterexamples

A conditional statement and its converse do not always share the same truth value. A statement can be completely true while its converse is completely false.
To show that a converse is false, you only need to provide a single counterexample — one specific instance where the new hypothesis is true, but the conclusion fails.