I know that if the 2 angles of a triangle are the same, it is isosceles. But what if the two sides are the same? Can we conclude that the corresponding angles are the same and it is isosceles?
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$\begingroup$It is by definition, from Greek isoskeles "with equal sides," from isos "equal" + skelos "leg".
$\endgroup$ $\begingroup$Yes. Assume $AC=BC$. Then triangles $ABC$ and $BAC$ are congruent (SAS), hence $\angle A=\angle B$.
$\endgroup$ $\begingroup$Yes, you can use the fact that given a triangle A,B,C if $\alpha$ is the opposite angle of BC, $\beta$ the opposite angle of AC and $\gamma$ opposite to AB it holds $$\frac{BC}{\sin {\alpha}}=\frac{AC}{\sin {\beta}}=\frac{AB}{\sin {\gamma}}$$ but i bet there is a simpler proof that doesn't use trigonometry. By the way i thought that having two equal sides was the definition of isosceles; while it's equivalent i've never heard your definition.
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