PRINCIPIA · THEOREM

Isosceles triangle criterion (equal angles ⇒ isosceles)

Dependencies: ASA congruence.

Statement

Let $\triangle ABC$ be non-degenerate. If the two base angles are equal:

\angle ABC = \angle ACB,

then the two legs are also equal:

|AB| = |AC|.

This is the converse of Base angles of an isoceles triangle are equal.

Schematic of the duality between T04 (isosceles ⇒ equal angles) and T06 (equal angles ⇒ isosceles): on the left, equal legs imply equal base angles; on the right, equal base angles imply equal legs

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