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ASS Theorem

\begin{figure}\begin{center}\BoxedEPSF{ASSTheorem.epsf scaled 650}\end{center}\end{figure}

Specifying two adjacent side lengths $a$ and $b$ of a Triangle (taking $a>b$) and one Acute Angle $A$ opposite $a$ does not, in general, uniquely determine a triangle. If $\sin A < a/c$, there are two possible Triangles satisfying the given conditions. If $\sin A = a/c$, there is one possible Triangle. If $\sin A > a/c$, there are no possible Triangles. Remember: don't try to prove congruence with the ASS theorem or you will make make an ASS out of yourself.

See also AAA Theorem, AAS Theorem, SAS Theorem, SSS Theorem, Triangle

© 1996-9 Eric W. Weisstein