The converse theorem

Characterising a locus actually requires proving two implications: the direct one and the converse one. But beware: the converse of a theorem is not always true.

Remark — Converse theorem

The converse theorem of “If $a$ then $b$” is “If $b$ then $a$”. Not all theorems have a valid converse.

Example: “university lecturer $\implies$ graduate” is true, but “graduate $\implies$ university lecturer” is false.

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Topics: Euclidean geometry
Concepts: Proof · Converse theorem
Skills: Proving