Proof: By Euclid
(related to Corollary: A Criterion for Isosceles Triangles)
"\(\Rightarrow\)": Let a triangle be isosceles. Then, by virtue of Prop. 1.5, the angles at its base are equal.
"\(\Leftarrow\)": Let the angles at the base of a triangle be equal. Then, by virtue of Prop 1.6 it is isosceles.
∎
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"