Key Concepts: Isosceles and Equilateral Triangles

Isosceles Triangle Theorem

If two sides of a Triangle are congruent, then the angles opposite those sides (base angles) are congruent.

Converse of Isosceles Triangle Theorem

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

Equilateral Triangle Corollaries

• A Triangle is equilateral if and only if it is equiangular.
• Each Angle of an Equilateral Triangle measures 60°.

Parts of an Isosceles Triangle

• Legs: The two congruent sides.
• Base: The non-congruent side.
• Vertex Angle: The Angle between the two legs.
• Base angles: The angles opposite the legs (always congruent).