Isoceles ⇒ equal angles — Base angles of an isoceles triangle are equal · Principia

Dependencies: SAS congruence.

Statement

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

|AB| = |AC|,

then the two base angles are also equal:

\angle ABC = \angle ACB.

By convention, $A$ is called the apex vertex, and $\angle B$ and $\angle C$ are called the base angles.

$Isosceles diagram: view \triangle ABC and \triangle ACB with the letters re-ordered as two triangles — geometrically the same figure, with B and C swapped; SAS immediately gives congruence ⟹ \angle B = \angle C.$

Base angles of an isosceles triangle are equal

Statement

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