0
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ It defines an isosceles triangle $\endgroup$ – imranfat Nov 24 '16 at 4:24
  • $\begingroup$ @imranfat I see. Is there a name for this theorem? $\endgroup$ – The Pointer Nov 24 '16 at 4:25
  • 2
    $\begingroup$ That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`. $\endgroup$ – dxiv Nov 24 '16 at 4:25
  • 1
    $\begingroup$ @dxiv Got it. Thank you. $\endgroup$ – The Pointer Nov 24 '16 at 4:26
1
$\begingroup$

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 $|AC|=|BC|$.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

It is called "sides opposite equal angles".

| cite | improve this answer | |
$\endgroup$

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.