# Two sides of a triangle have equal length if the angles opposite them are equal. Is this true? If so, what is the theorem called?

I am told that two sides of a triangle have equal length if the angles opposite them are equal.

Is this true? If so, I would appreciate it if someone could tell me what the theorem called.

Thank you.

• It defines an isosceles triangle – imranfat Nov 24 '16 at 4:24
• @imranfat I see. Is there a name for this theorem? – The Pointer Nov 24 '16 at 4:25
• That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`. – dxiv Nov 24 '16 at 4:25
• @dxiv Got it. Thank you. – The Pointer Nov 24 '16 at 4:26

It's an immediate consequence of the ASA congruence theorem (or axiom?): A triangle with equal angles at $A$ and $B$ is congruent to itself under $(A,B,C)\mapsto(B,A,C)$, hence $|AC|=|BC|$.

It is called "sides opposite equal angles".