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

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## Examples of Converse Statements

Let $P$ be the statement:

which is trivially true.

$P$ can also be written:

*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:

which is false.

## Sources

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