Converse and Contrapositive Statements/Examples/Triangles of 2 and 3 Equal Sides

Examples of Converse Statements

Let $P$ be the statement:

If a triangle has $3$ equal sides, then it has $2$ equal sides

which is trivially true.

$P$ can also be written:

A triangle has $3$ equal sides only if it has $2$ equal sides

A sufficient condition for a triangle to have $2$ equal sides is for it to have $3$ equal sides

A necessary condition for a triangle to have $3$ equal sides is for it to have $2$ equal sides

The converse of $P$ is:

If a triangle has $2$ equal sides, then it has $3$ equal sides

which is false.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.5$: Theorems and Proofs