Isosceles triangle theorem

Math

Definition

A theorem stating that if two sides of a triangle are congruent (equal in length), then the angles opposite those sides are also congruent. The converse is also true: if two angles are congruent, the sides opposite them are congruent.

Examples

  • In a triangle with two sides of length 5, the base angles must be equal
  • An equilateral triangle is a special case where all three sides and angles are equal
  • Finding a missing angle in a triangle where two sides are marked congruent
Key Fact

If AB ≅ AC, then ∠B ≅ ∠C (base angles are congruent).

Related Terms

Triangles Triangle congruence postulates Two-column proofs

Study This Concept

Practice isosceles triangle theorem with free review games in these units:

Geometry Unit 4: Congruent Triangles