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Isosceles Triangle Theorem

What is the Isosceles Triangle Theorem?

The isosceles triangle theorem tells us that:

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

The angle opposite a side is the one angle that does not touch that side. See the image below for an illustration of the theorem.

isosceles triangle theorem

This theorem is useful when solving triangle problems with unknown side lengths or angle measurements. The theorem goes both ways, meaning we can:

  • Assume two angles are congruent from knowing two sides are congruent.
  • Assume two sides are congruent from knowing two angles are congruent.
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