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?

$\begingroup$

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.

$\endgroup$ 4

2 Answers

$\begingroup$

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 $|AC|=|BC|$.

$\endgroup$ $\begingroup$

It is called "sides opposite equal angles".

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy